coupling cold atoms to nanophotonics: a novel platform for ......1 vladimir state university named...

Coupling cold atoms to nanophotonics: a novel platformfor quantum nonlinear optics

D.E. Chang1

1ICFO - Institut de Ciencies Fotoniques, Mediterranean Technology Park,08860 Castelldefels (Barcelona), Spain; email: [email protected]

(Dated: February 14, 2013)

We show that cold atoms coupled to nanophotonic devices represent a novel interface to realizenew mechanisms for strong, controllable interactions between individual photons.

Techniques to controllably interface atoms with quantum optical fields form the basis for many appli-cations in quantum information science. For example, photons are convenient to relay information overlarge quantum networks, while atoms naturally are physical systems that can process and store thisinformation. Thus far, the available techniques to efficiently couple single photons with atomic mediafall into one of the following, mostly independent, categories: i) cavity quantum electrodynamics (QED),where atomic interactions with light are enhanced via a high-finesse cavity, ii) coherent coupling withatomic ensembles exhibiting large optical depths, and iii) the use of fields tightly focused to dimen-sions smaller than or approaching the scattering cross-section of a single atom. Although remarkableachievements have been made with all of these approaches, a robust, scalable technique remains elusive.

Recently, several groups have successfully demonstrated that cold atoms can be trapped near andinterfaced with nanophotonic systems, such as hollow-core photonic crystal fibers [1] and taperednanofibers [2–4]. The traps are well-characterized [2, 3, 5], and the nearly diffraction-limited trans-verse confinement of optical fields enables ∼ 10% coupling efficiency of a single atom to the fiber [2, 3].This has already led to remarkable observations of strong light-matter interactions using relatively fewatoms and low powers [1]. It has also been proposed that such techniques can be extended to highlyconfigurable photonic crystal waveguides [6]. Together, these efforts raise the intriguing possibility forfuture nanophotonic systems with tremendous figures of merit, wherein atom-light interactions can betailored nearly at will.

Here, we discuss recent efforts to develop novel techniques to realize strong, controllable atom-photonand photon-photon interactions, which take full advantage of the parameter space afforded by nanopho-tonic interfaces and are not based upon the extension of existing techniques. As a specific example, wediscuss a protocol to achieve “all-atomic” cavity QED [7], as briefly described below. First, we show thatalthough the single-atom coupling to guided modes of a nanophotonic waveguide might be relativelyweak, there exist collective modes of a trapped atomic ensemble whose coupling to light is enhanced bythe square root of the atom number,

√NA. While collective effects are generally well-known, special

consequences emerge in the nanofiber system when the atoms are trapped in a lattice. In particular, col-lective effects cause such a lattice to act as a near-perfect mirror for an incident field close to resonance.In analogy to cavity QED, we then demonstrate that two sets of atomic mirrors can form an effec-tive cavity, which can greatly enhance the coupling of a single, specially chosen “impurity” atom (ora few impurity atoms) positioned inside. We introduce a novel quantum spin model to describe theatom-light coupling, which allows one to exactly map the atom-nanofiber interface onto the simple andelegant Jaynes-Cummings model of cavity QED [8]. A unique feature of our atomic mirrors comparedto conventional cavities is that they have long relaxation times and are highly dispersive. Remarkably,even with very low mirror finesse (F ∼ 102), this property allows one to attain the “strong coupling”regime of cavity QED, where vacuum Rabi oscillations [9–12] occur between an excited impurity atomand a single “photon” stored in the cavity (or more precisely, in the atomic mirrors). Furthermore, asquantum mechanical objects, these atom mirrors can be used to store quantum information and transferthis information into propagating waveguide modes. These various features can be combined to realizeall of the building blocks for scalable quantum information processing.

[1] M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M.D. Lukin.Efficient All-Optical Switching Using Slow Light within a Hollow Fiber. Phys. Rev. Lett. 102, 203902(2009).

[2] K. P. Nayak, P. N. Melentiev, M. Morinaga, F. Le Kien, V. I. Balykin, and K. Hakuta. Optical nanofiberas an efficient tool for manipulating and probing atomic fluorescence. Opt. Express 15, 5431 (2007).

2

[3] E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel. Optical Interface Createdby Laser-Cooled Atoms Trapped in the Evanescent Field Surrounding an Optical Nanofiber. Phys. Rev.Lett. 104, 203603 (2010).

[4] A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J.Kimble. Demonstration of a state-insensitive, compensated nanofiber trap. Phys. Rev. Lett. 109, 033603(2012).

[5] C. Lacroute, K. S. Choi, A. Goban, D. J. Alton, D. Ding, N. P. Stern, and H. J. Kimble. A state-insensitive,compensated nanofiber trap. New J. Phys. 14, 023056 (2012).

[6] C.-L. Hung, S. M. Meenehan, D. E. Chang, O. Painter, and H. J. Kimble. Trapped Atoms in One-Dimensional Photonic Crystals. arXiv:1301.5252 (2013).

[7] D. E. Chang, L. Jiang, A. V. Gorshkov, and H. J. Kimble. Cavity QED with atomic mirrors. New J. Phys.14, 063003 (2012).

[8] E. T. Jaynes and F. W. Cummings. Comparison of quantum and semiclassical radiation theories withapplication to the beam maser. Proc. IEEE 51, 89 (1963).

[9] J. J. Sanchez-Mondragon, N. B. Narozhny, and J. H. Eberly. Theory of Spontaneous-Emission Line Shapein an Ideal Cavity. Phys. Rev. Lett. 51, 550 (1983).

[10] R. J. Thompson, G. Rempe, and H. J. Kimble. Observation of normal-mode splitting for an atom in anoptical cavity. Phys. Rev. Lett. 68, 1132 (1992).

[11] M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche. QuantumRabi Oscillation: A Direct Test of Field Quantization in a Cavity. Phys. Rev. Lett. 76, 1800 (1996).

[12] R. Miller, T. E. Northup, M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble. Trapped atoms in cavityQED: Coupling quantized light and matter. J. Phys. B 38, S551 (2005).

��

Paolo Mataloni

Dipartimento di FisicaSapienza Università di Roma

��

��

��

��

��

!��

��

��

�� "�� !��

��#��$��

�� %��

��

&�� '��

��

��'��

��(��

Bose-Einstein condensation for trapped atomic polaritons

in a biconical waveguide cavity

A. P. Alodjants1,2

, I. Yu. Chestnov1, S. M. Arakelian

1

1 Vladimir State University named after A. G. and N. G. Stoletovs, Gorky str. 87, 600000, Vladimir, Russia2 Russian Quantum Center, 100Novayastr.,143025, Skolkovo, Moscow region, Russia

E-mail: [email protected].

The problem of high temperature Bose-Einstein condensation of atom-light polaritons in a

waveguide cavity was studied. Polaritons occur due to interaction of two-level atoms with

non-resonant quantized optical radiation, in the strong coupling regime, in the presence of

optical collisions with buffer gas of a very high pressure (500 bar). We propose a special

biconical waveguide cavity, permitting localization and trapping of low branch polaritons. We

have shown that critical temperature of BEC occurring in the system can be high enough

few hundred Kelvins.

1. Biconical waveguide cavity

In the paper we discuss an approach to reach a high (room and beyond) temperature phase transition with mixed

matter-field states polaritons in an atomic medium. In this system thermal equilibrium of coupled atom-light

states can be achieved experimentally with the help of optical collisions (OCs) with buffer gas atoms [1]. In

particular, we propose to use special biconical waveguide cavity (BWC) for trapping the polaritons inside. The

lifetime of photon-like low branch (LB) polaritons trapped in the waveguide can be longer than the

thermalization time, and is mainly determined by the cavity Q-factor. Thus we expect in such a waveguide that

for a large and negative atom-field detuning a high-temperature second order phase transition for polaritons

can be reached [2].

Fig. 1.Biconical metallic waveguide cavity for photon confinement and polariton trapping. The typical waveguide parameters are:

0 / 2.61 0.3R m ,1/ = 0.0005 1m .

Let us consider the problem of photon and polariton confinement in BWC, sketched in Fig.1. Waveguide

radius depends on z as 0( ) = / [1 | | ]R z R z ,with 0 and 0 , where characterizes the curvature of

waveguide profile. We assume that ( )R z is slowly varying with z coordinate, i.e. condition 1dR dz is

fulfilled. Such a form of waveguide corresponds to the simplest profile of a metallic waveguide, that is easier to

fabricate by using temporal technologies, cf. [3].

Omitting lengthy but straightforward calculations for field distribution in BWC one can arrive at transversal

k component of wave vector for TM-modes in the waveguide in the form , ( ) = ( )mp mpk z g R z , where mpg is

p -th zero of Bessel function ( )mJ x of the m -th order. Here we have used boundary conditions for electric

field components, taking ( ( )) = 0mJ k R z . Now it is easy to establish a dispersion relation ph( ) =k ck for the

photons in BWC: 2 2

ph ph cutoff ph ph/ 2zE k m V , (1)

where ph 0= mpm g R c is a mass of photon inside the BWC; 2cutoff ph= /m c represents a cutoff frequency

corresponding to the minimal photon energy. The last term 2ph ph 0( ) = | | | |V z m c z V z characterizes an

effective trapping potential for the photons inside the BWC.

One can intoduce polariton trapping potential, that is similar to photon one

pol( )U z U z , (2)

where pol 0 0 0/ 2R RU V and 1/22 2

0 = 4R is zero-momentum Rabi splitting frequency and

is atom-filed coupling parameter.We here mostly are interested in the case of = 1 . For the case of a

relatively small variation of the waveguide diameter over the length l of the waveguide, i.e. 0.5 1l , one

may use a linear variation of the diameter 0( ) 1 | |R z R z , which gives the desired potential in first order

approximation .

2.BEC of polaritons in BWC

Here we confine our analysis to 1D Bose-gas of LB polariton formed under the interaction of two level atoms

and field inside BWC in the presence of OCs [4]. We consider LB polaritons with relatively small momentum

zk at the center of the trap with an effective mass 360pol ph

0

22.8 10R

R

m m kg that is close to

photon mass. It is possible to show that the role of polariton-polariton scattering processes is negligibly small in

this limit, cf. [4]. Thus, we treat LB photon-like polaritons as one-dimensional ideal bosons confined in the

potential similar to (2).

The conditions for the observation of LB polariton BEC could be formulated in a general form and look like

0,n B RE k T (3)

where polnE is the energy spacing between longitudinal cavity polaritonic modes; pol is some

frequency characterizing polariton ``particle'' oscillation inside trapping potential (2) that will be determined

below.

The first constraint in (3) represents the condition for a quasiclassical limit where the energy spacing nEof quantized polaritonic states is essentially smaller than the thermal energy and the states may be treated as a

continuum. The second condition implies that the thermal energy is not enough to excite lower branch polaritons

to the upper branch, allowing us to neglect the upper branch.

In quasiclassical approximation (3), the critical temperature of true BEC of LB polaritons approaches

2/3

pol pol pol= 0.613B Ck T N U m . Below the critical temperature CT the occupation of the ground state is

then determined by 0 pol= 1 / .CN N T T Due to photon-like character of polaritons the total average

number of LB polaritons polN is close to the number of photons in waveguide mode phN . Under the low density

limit, where polaritonic model is acceptable see [2], phN is essentially smaller than the average number of

atoms. For the given atomic density 16= 10atn cm-3 the number of atoms interacting with photons is defined by

a mode volume, which is small enough about 0.5 μm3 which corresponds to approximately 5000 atoms inside

a waveguide cavity. It means that photon number phN being at least 10 times smaller is about 500. So, for

critical temperature one can obtain up to a thousand of Kelvins to observe BEC phenomena with polaritons in

our system. The main reason for the high transition temperature is the photonlike character of low branch

polaritons (i.e., their low effective mass). This, together with the thermalization due to optical collisions, may

allow to experimentally observe a high-temperature phase transition of dressed-state polaritons using realistic

parameters.

3. References

[1] I. Yu. Chestnov, A. P. Alodjants, S. M. Arakelian et al., “Thermalization of coupled atom-light states in the presence of optical

collisions”, Phys. Rev. A 81, 053843 (2010).

[2] A. P. Alodjants, I. Yu. Chestnov, and S. M. Arakelian, “High-temperature phase transition in the coupled atom-light system in the

presence ofoptical collisions”, Phys. Rev. A 83, 053802 (2011).

[3] U. Vogl, A. Saß, F. Vewinger et al., “Light Confinement by a Cylindric Metallic Waveguide in Dense Buffer GasEnvironment”, Phys.

Rev. A 83, 053403 (2011).

[4] I. Yu. Chestnov, A. P. Alodjants, S. M. Arakelian et al., “Bose-Einstein condensation for trapped atomic polaritons in a biconical

waveguide cavity”, Phys. Rev. A 85, 053648 (2012).

Revealing interference by continuous variable discordantstates

G. Brida,1 I. P. Degiovanni,1 M. Genovese,1 A. Meda,1 S. Olivares,2, 3 and M. G. A. Paris2, 3

1INRIM, Strada delle Cacce 91, I-10135 Torino, Italy2Dipartimento di Fisica, Universita degli Studi di Milano, I-20133 Milano, Italy

3CNISM UdR Milano Statale, I-20133 Milano, Italy

Abstract: We analyze properties of Gaussian states with peculiar quantum optical correlation properties toapply them even under scenarios that exceed the standard classification of quantum states into entangled andseparable, like the one based on the use of the parameter discord.

1. IntroductionStudying correlations among quantum systems is of key relevance in quantum information and quantum metrology

since they offer the possibility to perform measurements of practical interest, expanding the measurement capa-

bility beyond the classical limits. Different quantities and strategies to distinguish whether correlations have a

quantum nature or not have been introduced. In the quantum information framework, quantum discord set by def-

inition the boundary between entanglement and classical correlations, even if response is sometimes incompatible

with the physical one based on the Glauber-Sudarshan approach [1, 2]. A paradigmatic example in quantum optics

is given by a thermal equilibrium state divided at a beam splitter (BS). This kind of state belongs to the general

family of Gaussian states [3] characterized by Gaussian Wigner functions. It is indeed a classical state according

to the Glauber-Sudarshan theory; however, the bipartite state emerging from the BS displays non-zero discord and,

thus, form the informational point of view it contains a non-vanishing amount of quantum correlations. However,

in the particular case of Gaussian states, the only bipartite states with zero discord are the factorized ones [4]. This

means that if a factorized state �12 = �1 ⊗ �2 undergoes a unitary interaction described by the operator U12 (as

the one induced by a beam splitter, BS), then the evolved state �12 = U12�12U†12 may be correlated. This state

can be exploited in quantum information and imaging protocols, as ghost imaging with thermal light. Therefore

the dynamics of correlations in split thermal light has to be properly characterized. In fact, there is an exception

to the expected behavior. If we mix two identical Gaussian states in the beam splitter, no correlations appear,

as the interference of the two beams had not took place. On the other hand, since physical phenomena do have

observable effects, and the beam splitter is there, the interference between the two beams should be revealed. In

our work, we present two methods to reveal interference and an application.

2. TheoryWhen the initial state �12 and the evolved one �12 are exited in the same factorized state, they cannot be discrimi-

nated. However, from the very physical point of view, the presence of the exchange interaction, really exchanges

the quanta belonging the different modes, but this occurs in such a way that the whole system evolves as the

interaction itself was not present.

Revealing interference is possible by adding an ancillary mode 3 correlated with one of the two beams, say

beam 2. More explicitly, it is sufficient that the bipartite state �23 has non zero Gaussian discord to reveal the

interference between mode 1 and 2 even when the local states �2 = Tr3[�23] ≡ �1 are identical and the interaction

at the BS is not creating any correlations between them. In general, a Gaussian state � is fully characterized by its

2× 2 covariance matrix (CM), σ

[σ]hk =1

2〈RhRk +RkRh〉 − 〈Rh〉〈Rk〉 (1)

k = 1, 2, and first moment vector XT

= 〈RT 〉 =√2(�e[α],m[α]), with 〈A〉 = Tr[A�], where RT =

(R1, R2) ≡ (q, p) and q = (a+ a†)/√2 and p = (a− a†)/(i

√2) are the position- and momentum-like operators.

In the following, according to the requirements of the performer, we set α = 0,

The 6× 6 CM of the initial state �123 = �1 ⊗ �23 reads:

Σ123 =

⎛⎝ σ1 0 0

0 σ2 δ230 δT23 σ3

⎞⎠ , (2)

where σk is the 2 × 2 single-mode CM of mode k = 1, 2, 3, σ1 = σ2 = σ(N, β), N being the total number of

photons per mode, and the matrix δ23 = 0 contains the correlations between modes 2 and 3. After mixing mode

1 and 2 at the BS we have:

2

Σ123 → Σ(out)123 =

⎛⎝ σ 0

√1− τ δ23

0 σ√τ δ23√

1− τ δ23√τ δ23 σ3

⎞⎠ . (3)

where τ is the transmittance of the BS. The comparison between Eq. (2) and Eq. (3) shows that while the states

of modes 1 and 2 are (locally) left unchanged and, in turn, uncorrelated, both modes 1 and 2 are now correlated

with mode 3 (again, the presence of non-zero off-diagonal blocks denotes the presence of correlations between

the corresponding modes).

In order to have a deeper insight into this issue, we also exploited the polarization degree of freedom of the

interfering beams. We assume that the initial states have orthogonal polarizations, namely, mode 1 is horizontally

polarized (H), i.e., �(H)1 , while mode 2 is vertically polarized (V ), �

(V )2 (we assume that mode 3 has the same

polarization as mode 2). Indeed, due to the different polarizations, modes 1 and 2 do not interfere at the BS,

but give rise to two couples of collinear, superimposed correlated beams. In this case, due to the orthogonal

polarization, the two initially uncorrelated beams gains correlation after the interaction for the input beams and

the output beams. After the interaction, all the beams are projected to the 45◦ polarization basis From theory,

its emerge that the erasing of information about polarization affects correlations between beam 1 and 2, where

the correlation in absence of polarization control at the output of the BS and due to the mode mixing of the BS

vanishes when the information about initial polarization is lost. In our work, we perform both the experiments and

analyze in detail the dynamics of the correlations in mode mixing in the BS.

[1] R. Glauber, Phys. Rev. 131, 2766 (1963).[2] E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).[3] G. Adesso and A. Datta, Phys. Rev. Lett 105, 030501 (2010).[4] P. Giorda and M. G. A. Paris, Phys. Rev. Lett. 105, 020503 (2010).

Stimulated Raman processes under conditions

of radiation trapping

L.V. Gerasimov, M.D. Havey, I.M. Sokolov, D.V. Kupriyanov

Department of Theoretical Physics, St-Petersburg State Polytechnic University, 195251 St-Petersburg, Russia Physics Department, Old Dominion University, Norfolk, VA-23529, USA

e-mail: [email protected]

Abstract: We consider the stimulated Raman process when the scattered mode is trapped on a

dipole-closed atomic transition and can only diffusely escape the atomic sample. This

enhances the coupling strength for the light atom quantum interface and can attain the

random lasing regime.

Light transport in an ultracold and dense atomic gas has been intensively explored in experiment and theory

over the past decade. In atomic physics, original efforts were primarily directed towards study of complex

quantum systems, such as Bose-Einstein condensates, optical lattices, and localization phenomena, etc. These

have stimulated a vast amount of innovative research in a wide range of areas including quantum optics,

precision measurements and quantum information science [1]. We focus here on the problem of a light-matter

quantum interface suggesting that the light transport in a medium can be additionally controlled by certain

coherent mechanisms. As has been recently pointed out, see [1], the light propagation through an atomic sample

under multiple elastic scattering process could be coherently controlled with an external mode and implemented

as a mechanism of atomic memories, which potentially would be more effective than the standard protocols

assuming a one-dimensional propagation channel.

In the present report we consider the complementary configuration when a quantum spin state is originally

encoded in the spin subsystem of a disordered atomic ensemble. In the case of alkali-metal atoms this could be

modeled and experimentally demonstrated by coherent microwave excitation in the ground state hyperfine

sublevels but in a more general situation could realize any type of quantum state including those that are spin

squeezed or entangled with another distant atomic system. With turning on the coherent optical mode the

combination of microwave and optical fields initiates the stimulated Raman process. If this process evolves in

the hyperfine manifold of D2 line of an alkali-metal atom then the scattering mode can match the frequency of a

dipole-closed atomic transition such that the scattered light becomes trapped and shielded from its direct

propagation. The relevant energy levels and transition scheme are shown in the figure below for the example of 85

Rb:

Figure: (left) Energy levels and the excitation diagram for the Raman process; (right) Monte-Carlo simulation of

the light transport (from the central point of an atomic cloud at the resonance frequency of the F0=3->F=4

transition) controlled by a Raman process as function of the scattering orders n: (black) without coherent control;

(blue) with the presence of only optical mode c ; (red) with the control by both the optical c and microwave modes. The spontaneous losses on the F=3,2->F0=3 transition were eliminated for this round of calculations.

We consider the scattering dynamics by making complete Monte-Carlo simulations of the Raman process in

such radiation trapping conditions. The transformation of the correlation function of the scattered light escaping

the sample can be subsequently followed via iterative solution of the self-consistent Bethe-Salpeter equation.

This lets us track the diffusive transport, the stimulated amplification and the losses associated with the inverse

anti-Stokes scattering channel.

As we show in some specific conditions the system can demonstrate the so- effect,

which is an example of laser generation in the disordered system upon integrating both the amplifying and

feedback trapping mechanisms. Similar type of the random laser generation has been recently demonstrated in

experiment [2]. This effect is observable when the amplification dominates the losses and the gain requires

either population inversion between the upper states F=3,2 and the ground F0=3 state or elimination of the

spontaneous losses on the F=3,2->F0=3 transition. In the latter case we have optimal situation for the lossless

conversion of the spin state into the light subsystem. The right panel of the figure demonstrates the amplification

process upon approaching the random lasing threshold just for this case.

The proposed mechanism of coherent control of light diffusion is also discussed in the general context of a

light-atom quantum interface. The light subsystem maps the atomic state and in an ideal situation preserves all

the quantum correlations originally prepared in the atomic spin subsystem. That makes accessible the quantum

interface protocols if all the outgoing light is detected.

The work was supported by the CNRS-RFBR collaboration (CNRS 6054 and RFBR 12-02-91056) by NSF

(NSF-PHY-0654226 and NSF-PHY-1068159). D.V.K. would like to acknowledge support from an external

fellowship of RQC (Ref. number 86)

References

[1] J. Phys. B: At. Mol. Opt. Phys 45, 12 (2012), Special issue on quantum memory.

[2] Q. Baudouin, N. Mercadier, V. Guarrera, W. Guerin and R. Kaiser - arXiv:1301.0522 (2013)

A fluctuations estimations of the laser beams intensity in

a turbulent atmosphere

1Kuzyakov B.A.,

2Shmelev V.A.,

3Tihonov R.V.,

4Toptygin V.S.

1Candidate phys.-math. science, Moscow State Technical University of radio technical, electronics and automatics (MSTU MIREA), M., prospect Vernadskogo, 78; 2post-graduate student MSTU MIREA; 3post-graduate student MSTU MIREA; 4student MSTU MIREA

e-mail: [email protected]; [email protected]; [email protected]; [email protected] Abstract: A methods of a laser beams phase correction in a turbulent atmosphere are examined.

It is shown, that a method using of the orbital angular momentum states of photons, has the

substantial advantages.

At the present time, some systems allow you to create a failsafe wireless optical (AOLS) connection

between the various segments of a telecommunication channels, for example, local area networks Ethernet with

an adaptive variable velocity and energy depending on the condition of the optical path. AOLS transfer is

carried out in open space by a very narrow laser beam in the conditions of direct visibility [1-2]. Despite great

demand, AOLS it isn't free from some shortcomings connected with the atmosphere. Generally, in the size of

weakening of passable radiation various factors make a contribution. On optical properties of the atmosphere,

water in gas and liquid phases, carbon dioxide, ozone, and also aerosols generally influence. Weakening of

radiation as a result of Rayleigh dispersion can be many times more, than molecular absorption. In the real

atmosphere all types of dispersion take place, its structure continuously changes because of turbulence. Besides,

the contribution of each of the listed factors strongly varies with height. The greatest dispersion of laser

bunches is observed at the heights up to 1000 m.

Along with it, for increase of adequacy of developed model, it is necessary to consider one more

characteristic the orbital angular moment (OAM) of photons at distribution in the turbulent atmosphere. It is

defined by a specific form of the wave front twirled along an axis of distribution. To the usual flat front of a

wave there correspond flat surfaces of wave fronts and perpendicular shooters everywhere are strictly parallel

each other. At the twirled electromagnetic wave can differ not only the torsion direction (against or clockwise),

but also twisted degree (a ratio between a step of a spiral and wave length). Such wave bears the impulse

moment and if whichever body absorbs it, the moment of an impulse will be transferred to it, and it will start

rotating. Regulating this parameter, in space of conditions of OAM it is possible to create a large number of the

channels working at the same frequency. In this regard, recently the analysis of opportunities of change of

properties of photons in the turbulent atmosphere [3-6] actively develops. The range of fluctuations of an

indicator of refraction, depends on external L0 and internal l0 of scales of turbulence and wave number ki in

the i direction (i = x, y).

The turbulence conditions distribution of the laser beams is described conveniently by the dimensionless

parameter Ds(2a). This parameter defines structural function of a phase of the spherical wave, calculated on the

size of an initial aperture. On the basis of results of numerical modeling with use of the parabolic equation [2]

dispersions of fluctuation of intensity were calculated on axes of the focused Gaussian bunch and its effective

size in the turbulent atmosphere depending on dimensionless parameter:

Ds (2a) = 1,1 Cn2

k2 L (2a)

5/3 , (1)

here, L is the length of the route; a - initial radius of the beam; k=2 / is the wave number; Cn2 - structural

characteristic of the turbulent atmosphere.

To decrease the influence of turbulence on the stability (wrongness) of a channel of information transfer in the

atmosphere several methods are used. The most prevalent was the method of the wave front correction

Shark - Hartmann (MSH) and the method of correction phase (MCP), which uses the state of the photons orbital

angular momentum (OAM) [3]. A high sensitive Hartmann wave front sensors in SH is used,

correspondingly, which are sent to the control of adaptive optics for adjustment of the telecommunication

system. In the other method, a stream of photons with certain mode of OM is used in the MCP. The photons

with an appropriate fashion OM are selected in the receiver module. A such procedure allows to implement

adjustment of telecommunication systems.

On the basis of the carried-out calculations (fig.1) and the analysis of works [3-6] it is possible to note that

relative stability of the telecommunication channel decreases in a strong measure with a growth of turbulence of

the atmosphere. Also this analysis can be noted, that the use of the MCP leads to the improvement of correction

of the system of telecommunications, in comparison with SH in the whole range of variations of the Cn2 :

from 1E-16 to 1E-12. So, for example, when C-1 corresponding to 1E-12 (identified by a vertical bar with a

dashed line in fig. 1), relative stability of telecommunication channels at the MCP increases to 0.52

(intersection point of vertical bar and curve 3) in comparison with 0,25 for SH (intersection point of

vertical bar and curve 2) and in comparison with the amount 0.15 (intersection point of vertical bar and

curve 1) for systems without correction.

Fig. 1. Comparison of the relative stability dependences from Cn

2 of the telecommunication channel when using OAM states of photons

in a turbulent atmosphere with notes of corrections and ICF (C-1- a selected level example of the atmosphere turbulence): 1 - without correction, 2 - using SH, 3 MCP

In conclusion it can be noted that the relative stability of the telecommunication channel, associated with the

dispersion of the fluctuations of interest-illumination intensity in the axis of the laser beam in a turbulent

atmosphere, you can increase the using methods of correction. Moreover, the MCP has substantial advantage in

comparison with an others considered methods.

References

[1] R.R. Parenti, J.M. Roth, J.H. Shapiro, F.G. Walther, J.A. Greco. Experimental observations of channel reciprocity in single-mode

free-space optical links . Optics Express, 20, 19, 21635-21644 (2012).

-space optical communications in

atmos , 20, 1, 452-461 (2012).

a

Commun., 281, 3395-3402 (2008).

of intensity in the axis of the laser

61 s.t.c. MSTU MIREA, 2, 49-54 (2012). [5] D.J. Sanchez, D. , 19,

25, 25388-25396 (2011).

6] V.A. Banah, I.N. Smalikho, A.V. Falits. g of distribution of

and ocean optics, 24, 10, 848-850 (2011).

Nonlinear Processes Responsible for mid-Infrared and

Blue Light Generation in Alkali Vapours

Alexander Akulshin1, Dmitry Budker

2, Brian Patton

2, and Russell McLean

1

1Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, PO Box 218, Melbourne 3122, Australia

2 Department of Physics, University of California, Berkeley, CA 94720-7300, USA E-mail: [email protected]

Abstract: The nonlinear processes responsible for frequency up- and down-conversion of

resonant low-intensity laser radiation in Rb vapour have been evaluated from the spatial and

temporal properties of blue and mid-IR light resulting from wave mixing.

1. Introduction

Nonlinear parametric and nonparametric processes in atomic media can produce new optical fields with

substantially different optical frequencies. Frequency conversion of low-intensity cw laser radiation of diode

lasers into highly directional blue and mid-IR light in Rb and Cs vapours [1-4] is an active area of research

because of potential applications in quantum information processing, underwater communication and remote-

detection magnetometry [5].

In this approach, the new field generation occurs without an optical cavity. Alkali vapours provide

not only high resonant nonlinearity, but also set strong spatial anisotropy for new-field generation. An atomic

medium driven by bi-chromatic laser radiation tuned close to ladder-type transitions, 5S1/2 3/2 and 5P3/2

5D5/2

5D5/2 6P3/2 transition. This mid-IR radiation can even be randomly directed in a dense atomic sample [6];

however, in the case of modest atomic density 13

cm-3

) and a pencil-shaped atom-light interaction

region, superfluorescence consists of collimated forward and backward radiation. Mixing of the forward

superfluorescence mode with the applied laser fields produces radiation at 420 nm in the co-propagating

direction only, satisfying the phase-matching relation: k1+k2=kIR+kBL, where k1,2 are the wave vectors of the

laser fields at 780 and 776 nm, while kIR and kBL nm radiation,

respectively.

2. Experimental results

In our studies the spectral width of the collimated blue light (CBL) has been found to be less than 2 MHz for a

wide range of experimental conditions [7]. The linewidth appears to be mainly determined by the spectral

properties of the laser radiation rather than the parameters of the atomic medium. The linewidth and optical

frequency of CBL remain unchanged to within the 0.5 MHz experimental resolution, despite at least two-fold

variations in the atomic density and in the intensity of each laser. The CBL frequency is found to be centered on

the 5S1/2 3/2

frequencies.

The effect of velocity selective hyperfine optical pumping on amplified spontaneous emission and

parametric wave mixing has been explored. The number of resonant atoms contributing to the nonlinear

processes can be increased or decreased by velocity-selective incoherent optical pumping produced by an

additional laser tuned to any open transition from the ground-state 5S1/2 level. For a wide range of atomic 10

cm-3

11

cm-3

) at least tenfold enhancement of the coherent and directional blue

radiation due to optical pumping has been observed. The parametric wave mixing in optically pumped Rb

vapours has been obtained at a cell temperature as low as 33.6 0C, corresponding to an atomic density of

10 cm

-3.

It has been shown that optical pumping also modifies the refractive index of the medium, perturbing the

phase matching condition which must be satisfied and, consequently, affecting the direction of the CBL. Thus,

parameters of co-propagating blue light, such as intensity, direction and divergence, can be controlled by optical

pumping and such control is an important step towards probing small numbers of atoms using this approach.

We have undertaken an experimental study of the spectral and spatial properties of both the mid-IR

and blue radiation generated in specially fabricated Rb vapour cells. In order to increase the atom-light

interaction time and the probability of velocity-changing collisions we have extended our investigations to

atomic ensembles contained in cells with anti-relaxation internal surface coating and a buffer gas. A cell with

paraffin anti-relaxation coating allows effects related to hyperfine and Zeeman optical pumping produced by an

additional laser to be emphasized. In our previous studies it was not possible to detect the mid-IR radiation

directly, and its characteristics had to be inferred, but in a cell with sapphire windows transparent for IR

radiation both the optical fields can be directly detected, as shown in Fig.1. Different spectral dependences of

the blue and mid-IR radiation reflect their different origin.

-200 -100 0 100 200 3000.0

0.2

0.4

0.6

0.8

1.0

Blue LightN

orm

aliz

ed in

tens

ity

Frequency detuning (MHz)

mid-IR radiation

Fig. 1. Normalized intensity of co-propagating blue and mid-IR radiation as a function of the frequency offset of the 776 nm laser from the two-photon transition at fixed frequency of the

780 nm laser locked to the 5S1/2 5P3/2

We have found that the divergence of the co-propagating blue and mid-IR light is similar

(approximately 6 mrad) and determined by the collimation of the applied laser light. The backward mid-IR

radiation is weaker and more divergent (~14 mrad). Also the forward and backward mid-IR superfluorescence

have different dependences on the laser detunings.

3. Conclusion

There is substantial interest in enhancing efficiency of laser remote sensing. Backward directional and efficient

emission may constitute a novel approach to the problem. Further investigation of this and other nonlinear

schemes based on resonant wave mixing and understanding the role of various parametric and nonparametric

processes in dilute atomic samples should also determine the usefulness of this idea for laser-guide-star

techniques [8]. This scheme could also be used for generation of coherent and correlated fields at wavelengths

that are difficult to access with other methods.

4. References

-conversion in resonant coherent media , Phys.

Rev. A 65(5), 051801 (2002).

[2] A. M. Akulshin, R. J. McLean, A. I. Sidorov -wave 17(25) 22861, (2009).

ent 455 nm beam production in a cesium vapor , Opt. Lett. 34, 2321 (2009).

[4] G. Walker, A.S. Arnold, S. Franke- -Spectral Orbital Angular Momentum Transfer via Four-Wave Mixing in Rb

108, 243601 (2012).

[5] Proc. Nat. Acad. Science 108, 3522 (2011).

Phys. Rev. Lett. 82, 4420 (1999).

[7] A. Akulshin, Ch. Perrella, G-45, 245503 (2012).

[8] W. Happer, G. J, -turbulence compensation by resonant optical backscattering from the sodium layer in the upper atmosphere , Opt. Soc. Am. A11, 263 (1994).

Quantum simulator using atoms and photons in a hollow core fiber

L. C. Kwek

Centre for Quantum Technologies, National University of Singapore, Singapore 117543

Institute of Advanced Studies (IAS), Nanyang Technological University, Singapore 639673 and

National Institute of Education, Nanyang Technological University, Singapore 637616

To circumvent the limitations of conventional computers in tackling complex physical pro-

cesses, Richard Feynman proposed nearly thirty years ago a means of using well-understood

quantum systems called quantum simulators (or quantum emulators) to emulate similar,

but otherwise poorly understood, quantum systems. Among the various physical systems

that could be used to build a quantum simulator, one possibility is the use of regular ar-

rays of atoms or ions that are held in place by laser fields. In this talk, we describe how a

quantum simulator is also possible through photons propagating through a nonlinear optical

waveguide and interacting with cold atomic ensemble placed inside the fiber.

To be presented in ICONO 2013

Short Biography

LC Kwek is currently the Immediate Past President of the Institute of Physics Singapore

and a Principal Investigator at the Center for Quantum Technologies Singapore. He is also

the current Deputy Director (Physical Sciences) at the Institute of Advanced Studies at the

Nanyang Technological University. He is an elected Fellow of the American Association for

the Advancement of Science (AAAS) and a Fellow of the Institute of Physics UK. He is also

the immediate Past President of the Institute of Physics, Singapore and a Council Member

of the Association of Asia Pacific Physical Societies (AAPPS).

Coherent Effects in Resonance Gas of Cesium or Rubidium Diatomic Molecules

Vladimir A. Sautenkov1, 2, Sergei A. Sahakian1, Alexander M. Akulshin 1, 3, Boris B. Zelener1, 4

1 Joint Institute for High Temperatures of Russian Academy of Sciences, Moscow, 125412 Russian Federation 2 P. N. Lebedev Physical Institute of Russian Academy of Sciences, Moscow, 119991 Russian Federation

3 Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Australia 4 National Research Nuclear University, Moscow, 115409 Russian Federation

[email protected]

Abstract: We study coherent effects such as electromagnetically induced transparency and four-wave mixing in cesium and rubidium diatomic molecules. Our observations demonstrate a possibility of the light storage and intensity squeezing in a gas of alkali molecules.

1. Introduction

The light storage under conditions of electromagnetically induced transparency (EIT) and four-wave mixing (FWM) were demonstrated on resonance transitions in atomic media [1, 2]. We propose to extend the research activity to alkali diatomic molecules. The absorption bands of the alkali molecules are covering visible and near infrared spectral ranges. For example, absorption bands B1

Πu - X1Σg

+ of cesium and rubidium molecules are covering wavelengths 755 - 810 nm and 650 - 720 nm respectively. These molecular spectra are very dense. Spectral intervals between the individual absorption lines are comparable with Doppler broadening (~ 1 GHz). Earlier Doppler-free resonances [3, 4] and EIT resonances [5] were observed in Cs2. We report results of studies of coherent effects like EIT and FWM in Cs2 and Rb2. The next step will be observation of the light storage in a gas of alkali molecules.

2. Experimental results

A high density alkali vapor is a thermodynamic mixture of two components: atomic and molecular gases. The ratio of the molecular number density and atomic number density is order of 10–2. To study coherent effects the external cavity diode lasers (ECDL) are used. In Fig. 1 curve (a) presents saturation resonances on Doppler-broadened absorption lines of rubidium molecules and curve (b) presents reference saturation resonances on D2 - line of 7Li atoms (λ = 671 nm).

-2 -1 0 1 2 3

(a)

Tra

nsm

issi

on

Frequency (GHz)

(b)

Fig. 1. Saturation spectra of rubidium molecules (a) and lithium atoms (b)

The frequency is defined as detuning from saturation resonance on the cycling transition F = 2 - F = 3 in the 7Li atoms. A typical spectral width of saturation resonances on the molecular transitions in Fig. 1 is 35(5) MHz . In the experiment the counter-propagating pump (20 mW) and probe (0.4 mW) beams with diameter 0.2 cm crossed at a small angle (< 10-2 rad) in the vapor cell. The cell temperature was 570 K. Estimated optical non-linearity allows get reasonable efficiency of FWM process. In the first experiments by using co-propagating laser beams we observed FWM signal with efficiency ~ 10-4. The power of each beam was 10 mW. The experimental parameters will be optimized in order to increase the FWM efficiency.

Also EIT resonances in alkali molecules were observed. A sub-natural EIT resonance in a gas of cesium molecules (λ = 780 nm) is shown in Fig. 2. The EIT is attributed to the long-lived ground state coherence in Λ-level scheme inside B1

Πu - X1Σg

+ band. The EIT resonance was observed by using co-propagating drive and probe beams from two independent ECDLs. The power of each beam was 1.5 mW. The cell temperature was 500 K.

-60 -40 -20 0 20 40 60

Tra

nsm

issi

on

Frequency (MHz)

Fig. 2. The narrow EIT resonance on Doppler-broadened background

The width of the EIT resonance is 4 MHz and this value is four times less than the natural width of the molecular transition 20(2) MHz. The width due to the finite interaction time is evaluated as 0.1 MHz. The collision induced decoherence, power broadening and laser frequency jitter contributed to the spectral width of the EIT resonance. Collision induced decoherence rate was measured at different pressures of the cesium vapor. Probably buffer noble gas can help to increase interaction time and reduce the spectral width of EIT resonance.

Our preliminary experimental results demonstrate that it can be possible to observe the light storage and intensity squeezing in a gas of alkali molecules. The broad and dense molecular spectra allow investigate coherent effects on many wavelengths in visible and near-infrared ranges.

3. References

[1] M. D. Lukin, “Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457 - 472 (2003).

[2] N. B. Phillips, A. V. Gorshkov, I. Novikova, “Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing,” Phys. Rev. A 83, 063823 (2011).

[3] U. Diemer, R. Duchowich, M. Ertel, F. Mehdizadeh, W. Demtrὅder, “Doppler-free polarization spectroscopy of the B1Πu state Cs2 ,” Chem.

Phys. Lett., 164, 419 - 426 (1989).

[4] H. Chen, H. Li, Y. V. Rostovtsev, M. A. Gubin, V. A. Sautenkov, M. O. Scully, “Near-infrared saturation spectroscopy of cesium molecules using diode laser,” JOSA B, 23, 723 - 726 (2006).

[5] H. Li, H. Chen, M. A. Gubin, Y. V. Rostovtsev, V.A. Sautenkov, M. O. Scully, “Observation of Electromagnetically Induced Transparency in Cesium Molecules,” Las. Phys. 20, 1725 - 1728 (2010).

Measurement of the Temperature of AtomicEnsembles via Which-Way Information

R. de J. Leon-Montiel and Juan P. Torres

ICFO-Institut de Ciencies Fotoniques, and Department of Signal and Theory and Communications, UniversitatPolitecnica de Catalunya, Castelldefels, 08860 Barcelona, Spain

[email protected]

Abstract: We unveil the relationship existing between the temperature of a threelevel atomic ensemble and the direction in which Stokes photons are spontaneouslyemitted when exciting the ensemble with an optical pulse. This relationship, whichis based on the amount of which-way information available concerning wherethe Stokes photons originated, allows us to devise a new scheme to measure thetemperature of atomic ensembles.

OCIS codes:Atomic ensembles are an invaluable tool for the implementation of quantum information protocols [1],or the generation of nonclassical photon pairs [2, 3]. In these “write-read” schemes, a weak optical pulseinteracts with an atomic ensemble leading to the spontaneous emission of a Stokes photon. Since the Stokesphoton and the atomic ensemble are highly correlated, the projection of the Stokes photon heralds thegeneration of an atomic state that is a coherent superposition of all possible states of the ensemble whereonly one atom has been excited (the collective atomic state).

In a room-temperature atomic ensemble, where atoms are considered to move fast within the cloud,Stokes photons are emitted within a small cone around the direction of propagation of the pump pulse [4,5],whereas in the case where atoms are considered to be fixed in their positions (cold atomic clouds), Stokesphotons have no preferred direction of emission [6], always that it is not forbidden by the transition matrixelements. These results consider only the angular distribution of emitted photons in two limiting cases:when atoms are either moving very fast (high temperature) or are completely fixed (low temperature)within the cloud.

The transition between these two cases has not been explored, yet. Here, we construct a model to describethe angular distribution of emitted Stokes photons as a function of the temperature of the atomic cloud. Byusing this model, we propose a new technique where the measurement of the width of the emission conecan be used to determine the temperature of the cloud.

Let us consider a cloud of N identical three-level atoms in a Λ configuration. The cloud is illuminatedby an optical pulse that couples the transition |g〉 → |e〉 with a detuning Δ. The spontaneous decay of theatom (|e〉 → |s〉) leads to the generation of a photon with different wavelength (Stokes photon). Before theinteraction, we consider that all the atoms are in the ground state and that there are no photons in the opticalmodes (i.e. |Ψ〉0 = |g1...gi...gN〉⊗ |0〉k). Assuming that the pump pulse is weak enough, so we can make useof first-order perturbation theory, we write the temperature-dependent state of the system atoms-photonas [7]

|Ψ〉= |Ψ〉0 − iε (Δω)N

∑i=1

∫dk

∫V

dr f (r,ri)u(r⊥)exp{−iΔk · r}|g1...si...gN〉 |k〉, (1)

where ε(Δω) =∫ t

0 dt ′g ξ (t ′)exp(iΔωt ′), with g being the coupling coefficient of the |g〉 → |s〉 transition, ξ (t)the temporal shape of the pump, with central frequency ω0 = k0c and transverse spatial shape u(r⊥). Δω =ω − (ω0 −ωsg) and Δk = k− k0z, where k is the wavevector of the Stokes photon, with frequency ω = |k|c,and ωsg is the transition frequency between states |g〉 and |s〉.

The new function f (r,ri) describes the movement of each atom around its mean position ri,

f (r,ri) =1

π3/2A3 (T )exp

[−|r− ri|2

A2 (T )

], (2)

where A(T ) = vaτ determines the radius of the area over which the atoms can move during the interactiontime. It depends on the pump pulse duration (τ), and on the speed (va =

√2KBT/m) most likely to be

(a)

PUMP

STOKES

DETECTORS

(b)

0 200 400 600 80010

100

1000

Emission cone (FWHM, mrad)

Tem

pera

ture

(μK

)

Fig. 1. (a) Proposed experimental setup. (b) Temperature of the atomic cloud as a function of the full width halfmaximum (FWHM) of the emission cone for different pulse durations. Solid line: τ = 10 μs; Dashed line: τ = 30

μs; Dash-dotted line: τ = 100 μs.

possessed by any atom of the system. m is the mass of the atom, KB is the Boltzmann constant and T is thetemperature of the atomic ensemble.

Using Eq. (1), we can find that the probability of emitting a Stokes photon in the direction k is given by

P(k) =N

∑i=1

|S (ri,k)|2 , (3)

where S(ri,k) =∫

V dr f (r,ri)u(r⊥)exp(−iΔk · r), with V being the volume of the cell that contains the cloud.The close relationship between the width of the emission cone and the temperature of the atomic

ensemble [Eq. (3)] allows us to put forward a new technique to determine the temperature of atomicclouds [7]. The proposed experimental setup consists of an array of detectors (or a movable detector) ableof detecting Stokes photons along different directions, as depicted in Fig. 1(a). By measuring the widthof the emission cone, we can make use of Eq. (3) to retrieve information about the temperature of theatomic ensemble. Figure 1(b) shows the temperature of the atomic ensemble as a function of the FWHMof the emission cone. Calculations were performed considering an ensemble of 87Rb atoms contained ina pencil-shaped cell with transversal dimensions: Lx = Ly = 2 mm, and length Lz = 30 mm. The atoms areilluminated by a pump pulse with a Gaussian transversal shape of radius r0 = 1 mm. The level configurationof the atoms is set to 52P1/2 for the excited level |e〉, and the Zeeman-splitting levels 52S1/2 (F = 1) and52S1/2 (F = 2) for the |g〉 and |s〉 states, respectively.

References

[1] L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linearoptics,” Nature (London) 414, 413 (2001).

[2] C. H. van del Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, “Atomic Memory forCorrelated Photon States,” Science 301, 196 (2003).

[3] A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photonpairs for scalable quantum communication with atomic ensembles,” Nature (London) 423, 731 (2003).

[4] L.-M. Duan, J. I. Cirac, and P. Zoller, “Three-dimensional theory for interaction between atomic ensembles and free-space light,”Phys. Rev. A 66, 023818 (2002).

[5] D. Porras and J. I. Cirac, “Collective generation of quantum states of light by entangled atoms,” Phys. Rev. A 78, 053816 (2008).

[6] M. O. Scully, E. S. Fry, C. H. Raymond Ooi, and K. Wodkiewicz, “Directed Spontaneous Emission from an Extended Ensemble ofN Atoms: Timing Is Everything,” Phys. Rev. Lett. 96, 010501 (2006).

[7] R. de J. Leon-Montiel and Juan P. Torres, “Measurement of the temperature of atomic ensembles via which-way information,”Phys. Rev. A 85, 033801 (2012).

��

�Paolo Tombesi

��

��

�

Abstract: A new protocol for distant parties entanglement certification is introduced to

avoid non-local measurement.

Let us suppose we need to transfer quantum information, generated inside a superconducting

coplanar wave-guide cavity, to a distant node of a quantum network where another superconducting

cavity is. Or, which is the same problem, we want to transfer the information from a

micromechanical resonator to another one very far away.

It is well known that the best carrier of information is surely the photon. However, it has to be

an optical photon, but in the superconducting cavity or with micromechanical resonators only

microwave photons or phonons can be obtained. Thus, one needs a quantum frequency converter

from microwave to optical frequency. The need to be quantum means that it should work at single

photon level.

In a couple of recent papers [1, 2] we proposed a device able to teleport microwave single

photons to optical frequency, and vice versa, with good fidelity. When the two nodes are very far

away, although the optical fiber used to send the quantum information has a very small loss, the

single photon cannot reach distances of the order of thousand kilometers without amplification.

Amplification is however forbidden because it introduces noise; then one has to resort in a quantum

repeater.

This device works, essentially, because of entanglement, which is a characteristic of quantum

states at the basis of the attractive and counterintuitive aspects of quantum mechanics.

A possible repeater could be a device able to swap the entanglement between parties that never

interacted. It means that the node A (Alice) and the far distant node B (Bob) both generate a

bipartite entangled state. One of their states is then sent to another node C (Charlie), let say in the

middle of the two distant nodes, where an appropriate measurement is made such that the two nodes

A and B have the remaining states entangled.

In this way a quantum channel is generated between the distant parties able to teleport any

unknown quantum state from A to B. The problem now is: how can we be sure that the two distant

parties have their remaining states entangled?

When the remaining states are at optical frequency one could send the states to the same middle

node C to perform an entanglement test, measuring some entanglement witness. However, in the

case of microwave remaining fields or, even worse, for micromechanical resonators, this is not

possible and one has to devise another strategy.

In this talk I will present one possible strategy, which consists in preparing the states in nodes A

and B in order to satisfy a new criterion. This criterion, which is called certification, consists in

using an ancillary optical field in both nodes, i.e. instead of the usual bipartite state use a tripartite

one, such that the purities of the tripartite states verify an inequality [3].

With this requirement, together with the fields for swapping, two ancillary fields are sent to

Charlie, who performs a measurement on them after the swapping operation. Then, based on the

result of this measurement one can locally certify that the two distant nodes A and B share an

entangled state, and a state teleportation from Alice to Bob becomes possible.

[1] Sh. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, Reversible Optical-to-Microwave Quantum Interface; Phys. Rev. Lett. 109,

130503 (2012);

[2] Sh. Barzanjeh, P. Tombesi, and D. Vitali Optical Single Photons on Demand Teleported from Microwave Cavities; arXiv: 1205.6461 to appear in

Physica Scripta

[3] M. Abdi, S. Pirandola, P. Tombesi, and D. Vitali Entanglement Swapping with Local Certification: Application to Remote Micromechanical Resonators Phys. Rev. Lett. 109, 143601 (201��

Majorana fermions in atomic wire networks and

topologically protected quantum computing

Mikhail A. Baranov

Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria;Institute for Theoretical Physics, Innsbruck University, A-6020 Innsbruck, Austria;

RRC "Kurchatov Institute", Kurchatov Square 1, 123182, Moscow, Russiae-mail address: [email protected]

Christina V. Kraus and Peter Zoller

Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria;Institute for Theoretical Physics, Innsbruck University, A-6020 Innsbruck, Austria

Abstract: I discuss topologically protected Majorana edge states in systems of fermionic atoms in

optical lattices: How one can create them, detect, braid, and use for a topologically protected

implementation of the Deutsch-Josza algorithm.

Summary

I discuss topologically protected Majorana edge states in systems of fermionic atoms in optical lattices: How one

can create them, detect, braid, and use for a topologically protected implementation of the Deutsch-Josza algorithm.

I consider a system of single component fermions that are confined to an array of finite one-dimensional wires.

The Hamiltonian includes nearest-neighbor hopping and pairing terms and a chemical potential. This form of the

Hamiltonian allows for a cold atom implementation: While the hopping term arises naturally in an optical lattice

setup, the pairing term can be realized by a Raman induced dissociation of Cooper pairs (or Feshbach molecules)

forming an atomic BCS reservoir.

This Hamiltonian supports zero energy Majorana fermions which are localized at the ends of each wire. Due to

their anyonic statistics, an interchange (braiding) of two Majorana modes results in the braiding unitary and is the

key step for realizing a topological quantum computation. In the proposed cold-atom implementation, I present a

protocol that allows realizing braiding by means of simple lattice operations on a few sites and links of the lattice,

which are based on the single site/link addressing available in cold atom experiments, and provide a careful study of

the full braiding dynamics including imperfections.

Although braiding of Majorana fermions do not allow to implement a complete set of quantum gates, it still can

be used to realize some algorithms. As an example, I demonstrate that the Deutsch-Josza algorithm for two qubits

can be realized with nine braiding operations. This demonstrates that the implementation of simple quantum

algorithms in atomic topological setups is within experimental reach.

��

�� 1. Departamento de Física, Universidade Federal de Pernambuco, 50.670-901 Recife, PE, Brazil, e-mail : [email protected]

2. Laboratoire Aimé Cotton, CNRS, Université Paris-Sud, ENS Cachan, 11, 91405 Orsay, France3. Laboratoire de Physique des Lasers, CNRS, Université Paris 13, F-93430 Villetaneuse, France

Abstract: We report on the storage and non-collinear retrieval of orbital angular momentum of light in an ensemble of cold cesium atoms. The stored and retrieved beams are shown to carrythe same orbital angular momentum.

1. Introduction

Light beams carrying orbital angular momentum (OAM) have attracted a great interest in the past few years

owing to their several applications, ranging from the mechanical manipulation of macroscopic particles to the

encoding of quantum information [1]. A well-known family of these beams is constituted by Laguerre-Gaussian

modes specified by a topological charge , which gives to the mode a helicoidal phase structure and a

corresponding OAM per photon equal to . The nonlinear interaction of these beams with atomic systems has

been investigated via four-wave mixing (FWM) processes and the corresponding conservation of OAM

demonstrated both in cold and thermal atoms [2,3]. The storage of OAM in cold and thermal atomic ensembles

was also previously demonstrated [4,5].

Differently from the previous observations, this work demonstrates that the stored OAM of a light beam can

be retrieved along a nearly non-collinear direction with great fidelity.

2. Experimental Setup and Results

The experiment is performed in cold cesium atoms, obtained from a MOT, using a time delayed FWM

configuration. Light beams with topological charges ℓ=0,1,2,3, produced by a spatial light modulator (SLM) are

incident into the medium along the z direction, as shown in the simplified experimental scheme depicted in Fig.

1-(a). The frequency of the beams is resonant with the transition 6S1/2, F=3 – 6P3/2, F=2. The phase structure of

the beam carrying OAM is stored into the Zeeman coherence grating induced by the incident writing beams Wand W’ that form a small angle (~2

0) between them and have opposite circular polarization. The writing beams

are kept on for a period of 30 μs, long enough to create a stationary Zeeman coherence grating. Then they are

switched off, as indicated by the time sequence shown in Fig. 1 (c) .

Fig. 1 ��

��

��

��

��

��

6P3/2, F=2

6S1/2, F=3

Ωw Ωw’ω0

0

W, W’

R

OFF

ON

ON

OFF

ts

Time

W

W’

RC

��

��

z

z'

Fm

1−Fm 1+Fm

��

ΩRΩC

Fm

1−Fm 1+Fm

-z'MOT MOT

-z

� ≠ 0 � = 0� ≠ 0� = 0

� = 0� ≠ 0

� ≠ 0� = 0

As shown in Fig. 1- (b), after the storage time ts, a reading beam R, counter-propagating to the writing beam

W and with opposite circular polarization, is turned on and the retrieved beam (C), whose propagation direction

is determined by the phase matching condition is monitored by a CCD camera.

In Fig. 2 (a)-(b)-(c) we show the images of the incident writing beam, obtained by retroflection right before

the MOT, for three different topological charges ℓ=1,2,3, and in Fig. 2 (d)-(e)-(f) the corresponding retrieved

beam images after a storage time tS = 2.0 μs. The donut shape is retrieved in the FWM process.

In order to reveal the topological charge, both in sign and magnitude, of the retrieved beam as compared to

that of the incident beam, we superposed the writing beam W with an auxiliary Gaussian beam with

approximately the same power but having a slightly different radius of curvature. Thus, by again retro-reflecting

the incident superposition with a mirror placed before the MOT we obtain the interference patterns shown in Fig.

2 (g)-(h)-(i). The corresponding interference patterns for the retrieved superposition are shown in Fig. 2 (j)-(k)-

(l) . By taking into account that a mirror reflection changes the sign of the topological charge, which determine

the sense of rotation of the spiral, and that the foci of the two incident beams generating the interference patterns

are both located before the atomic cloud, we conclude that the topological charge of the retrieved beam is

identical in magnitude, but with opposite sign to that of the incident W beam. Therefore, as these two beams are

nearly counter propagating they should carry the same OAM. These results clearly show that the OAM of the

incident beam has been stored in the atomic medium and then retrieved along a nearly different direction [6].

Additional results and discussions concerning the OAM conservation, as well as the manipulation of the

stored OAM with an additional magnetic field will also be presented. In particular, we have observed that the

grating decay time varies with the topological charge.

We thank CAPES-COFECUB (Ph 740-12) for the support of Brazil-France cooperation.

Fig. 2 Images of the incident and retrieved beams for different topological charges: (a)-(b)-(c) are the images of the

incident writing beam, respectively, for ℓ=1,2,3; (d)-(e)-(f) are the corresponding images of the retrieved beams; (g)-(h)-

(i) and (j)-(k)-(l) are the corresponding interference patterns with a Gaussian beam as described in the text.�

3. References�

[1] M Padgett, J��

[2] S. Barreiro and J. W. R. Tabosa, Generation of Light Carrying Orbital Angular Momentum via Induced Coherence Grating in Cold

Atoms, Phys. Rev. Lett. 90 133001 (2003)

[3]W. Jiang, Q. F. Chen, Y. S. Zhang, and G. C. Gao, Computation of topological charges of optical vortices via nondegenerate four-wave

mixing, Phys. Rev A 74, 043811 (2006).

[4] D. Moretti, D. Felinto, and J. W. R. Tabosa, Collapses and revivals of stored orbital angular momentum of light in a cold-atom ensemble,

Phys. Rev. A, 79, 023825 (2009)

[5]R. Pugatch, M. Shuker, O. Firstenberg, A. Ron and N. Davidson, Topological Stability of Stored Optical Vortices, Phys. Rev. Lett. 8,

203601 (2007)

[6] R. A. de Oliveira, L. Pruvost, P. S. Barbosa, D. Felinto, D. Bloch, and J. W. R. Tabosa, in preparation.

��

1=�

2=�

3=�

��

��

��

1,2 2 2

3 3 3

1

2

3

N N2

N4

Πl

σj

Plj = Tr{Πlσj}.

Plj fl

fl =∑j

xjPlJ

xj

ρ =N∑j=1

xjσj

ρxj

ρ

High Resolution Optical Time-Domain Reflectometry

using Superconducting Single-Photon Detectors

O. Minaeva1,2

, A. Fraine3, A. Korneev

2, A. Divochiy

2, G. Goltsman

2, A. Sergienko

3,4

1Department of Biomedical Engineering, Boston University, Boston, Massachusetts 02215 2Department of Physics, Moscow State Pedagogical University, 119992 Moscow, Russia

3Department of Electrical & Computer Engineering, Boston University, Boston, Massachusetts 02215 4Department of Physics, Boston University, Boston University, Boston, Massachusetts 02215

e-mail:[email protected]

Abstract: We discuss the advantages and limitations of single-photon optical time-domain

reflectometry with superconducting single-photon detectors. The higher two-point resolution

can be achieved due to superior timing performance of SSPDs in comparison with InGaAs

APDs. OCIS codes: 060.2270, 040.5160

It has been known in the literature that a single-photon optical time-domain reflectometry (OTDR)

outperforms conventional state-of-the-art OTDR in dynamic range and in two-point resolution

performance [1-4]. However, it has been shown that using InGaAs APDs in OTDR leads to

problematic dead zones due to afterpulsing and the charge persistence effect. Here we discuss how

superconducting single-photon detectors (SSPDs) could improve OTDR two-point resolution even

further by enhancing the timing jitter and by eliminating problems associated with dead zones that

usually accompany the use of InGaAs avalanche photodiodes.

The superconducting single-photon detector based on NbN nanowires has been developed about a

decade ago [5] and became a very popular choice for single-photon detection at telecom wavelengths.

The operation principle of such a detector is based on the local suppression of the superconductivity

in the narrow NbN stripe upon photon absorption. SSPD is a novel emerging solution for the infrared

single-photon counting featuring above 15% detection efficiency (DE) at 1550 nm wavelength with

10 s-1 dark counts rate, 40 ps timing jitter, and above 100 MHz counting rate [6]. SSPD is made of a

planar nanostructure patterned from 4-nm-thick NbN film deposited on an Al2O3 (sapphire) or a Si

substrate [7]. The sensitive element of the SSPD is 100-nm-wide NbN stripe. The stripe is shaped as a

meander covering a square area typically 10 um x 10 um with a filling factor above 0.5. This

facilitates an efficient coupling of the SSPD with a single-mode optical fiber.

One practical limitation of SSPDs is their low operating temperature. Detectors should be cooled

down to the liquid helium temperature (2-4K). Modern receivers based on the use of SSPDs have

become more practical as detectors can now be installed in a relatively compact closed-cycle helium

refrigerator or even into a helium-free cryogenic system. The SSPD-based receivers are currently

available as a commercial product [8].

Fig.1 Experimental setup for OTDR with SSPD

Here we discuss our results illustrating performance of a single-photon counting OTDR with

superconducting single-photon detectors. The experimental setup schematic is illustrated in Fig.1.

Optical pulses from the picosecond laser pass through the circulator towards the sample under test (a

piece of SM fiber). The reflected light from the fiber under test is redirected into another arm to the

SSPD thanks to the circulator.

The amplified signal from the SSPD is registered using a high-resolution timing correlator

(PicoHarp300). The electrical synchropulse from our ps laser is used as a “start” signal. To improve

the timing resolution, the optical signal from the laser could be split using a regular optical beam

splitter and the second single-photon superconducting detector could be used to generate a “start”

signal for the correlator.

The time delay between an original optical pulse injected into the fiber under test, and the return

pulse reflected from the fault in the fiber (or fiber connections) is evaluated during the OTDR

procedure. Our results on two point resolution measurements obtained with short pieces of telecom

fibers are presented in Fig.2. Two peaks due to insertion of the 22.0 cm and 22.7 cm long fibers have

been resolved. The ultimate two-point resolution will be dependent on the optical system timing

resolution that includes a laser pulse optical width and jitter as well as the single-photon detector

jitter. In our system demonstration we have measured <60 ps total timing resolution. This means that

the ultimate two-point resolution of OTDR with SSPDs can be as low as 6 mm in the telecom fiber.

This has been confirmed in the experiment (see Fig.2) where we have resolved 7mm difference in

fiber lengths.

7 mm resolution

Fig.2 Time histograms obtained with 21.8cm, 22.0 cm and 22.7 cm long fibers

SSPDs have a series of advantages in comparison with other single-photon counting detectors. Its

low timing jitter and higher signal to noise ratio will lead to a better two-point resolution. The higher

repetition rate and possibility to work in a free running mode (no gating) leads to shorter test times.

However, the main advantage of SSPDs for OTDR is the possibility to eliminate the dead-zone

problem that is well known in a single-photon counting OTDR with APD detectors. The effect of

afterpulsing creates significant problems in cases when the shorter fiber link must be evaluated with a

high precision. The SSPD detector does not have such afterpulsing problems and could be used in

situations where the high precision tests are required.

References: [1] Healey, P., Hensel, P., "Optical time domain reflectometry by photon counting," Electronics Letters , vol.16, no.16, pp.631-633 (1980)

[2] A. Lacaita, P. A. Francese and S. D. Cova, "Single-photon optical-time-domain reflectometer at 1.3 um with 5-cm resolution and high

sensitivity", Opt. Lett., vol. 18, no. 13, pp. 1110-1112 (1993)

[3] M. Wegmuller, F. Scholder, and N. Gisin, “Photon-counting OTDR for local birefringence and fault analysis in the metro environment,”

J. Lightwave Technol., vol. 22, no. 2, pp. 390–400 (2004)

[4] Patrick Eraerds, Matthieu Legré, Jun Zhang, Hugo Zbinden, and Nicolas Gisin, "Photon Counting OTDR: Advantages and Limitations,"

J. Lightwave Technol. 28, 952-964 (2010)

[5] A. Semenov, G. Gol'tsman, and A. Korneev, Quantum detection by current carrying superconducting film, Physica C, Vol. 352, pp. 349-

356 (2001)

[6] A. Korneev, V. Matvienko, O. Minaeva, I. Milostnaya, I. Rubtsova, G. Chulkova, K. Smirnov, V. Voronov, G. Gol’tsman, W. Slysz, A.

Pearlman, A. Verevkin, and R. Sobolewski, IEEE Trans. Appl. Supercond. 15, 571 (2005)

[7] W. Pernice, C. Schuck, O. Minaeva, M. Li, G.N. Goltsman, A.V. Sergienko, H.X. Tang, "High Speed Travelling Wave Single-Photon

Detectors With Near-Unity Quantum Efficiency", arXiv:1108.5299v1 (2011)

[8] http://www.scontel.ru/ps_reseivers.html

Information Transmission Capacities

of Hybrid Communication Channels

Alexander S. HolevoSteklov Mathematical Institute, Gubkina 8, 119991 Moscow, Russia

Email: [email protected]

Abstract: We compute and compare the classical entanglement-assisted capacity Cea and the unassisted capacity C for two classesof entanglement-breaking communication channels: measurementchannels give the most spectacular examples of the gain of entan-glement assistance: Cea/C � 1, while for state preparation channelsCea/C = 1, unless there is an (energy) constraint on the input ofthe channel.

The protocol of entanglement-assisted classical communication was intro-duced in the seminal paper of Bennett, Shor, Smolin and Thapliyal [1] as ageneralization of superdense coding to noisy quantum channels. An importantobservation was: entanglement-assisted communication may be advantageouseven for entan-glement-breaking channels such as depolarizing channel withsufficiently high error probability (see also [2], where a detailed description canbe found).

We provide further results in this direction by considering two distinguishedclasses of entanglement-breaking channels, namely measurements (quantum-classical or q-c) and preparations (classical-quantum or c-q). We use for themthe common name “hybrid channels”, for which we compute and compare the(unassisted) classical capacity C and the entanglement-assisted classical capac-ity Cea. In this talk based on recent papers [3, 4], we emphasize the case ofinfinite-level systems such as Bosonic continuous variables. In this case the in-put of the channel is subject to energy constraint, so that both capacities arefunctions of the maximal input energy E. Our conclusions are:

• Measurement channels, both constrained and unconstrained, give the mostspectacular examples of the gain of entanglement-assistance: Cea/C � 1.In particular for the measurements with pure posterior states the informa-tion loss in the entanglement-assisted protocol is zero, resulting in arbi-trarily large gain for very noisy or weak signal channels. This is illustratedby examples of continuous observables corresponding to state tomographyin finite dimensions and heterodyne measurement.

• On the other hand, unconstrained preparation channels are characterizedby futility of entanglement-assistance: Cea/C = 1. This property is pre-served under rather special input constraints, while for generic constraintstill Cea/C > 1. These statements are corroborated by considering ex-

1

plicit examples of channels representing classical signal with quadraticconstraint on the background of additive quantum vacuum noise.

In finite dimension a classical-quantum or quantum-classical channel canalways be represented as a quantum channel, by embedding the classical inputor output into finite-level quantum system. Then it makes sense to speak aboutentanglement-assisted capacity Cea of such a channel, in particular, to compareit with the unentangled classical capacity C. We first consider the case of q-c(measurement) channels, showing that generically C < Cea for such channels[3]. For infinite dimensional (in particular, continuous variable) systems anembedding of the classical output into quantum is not always possible, howeverentanglement-assisted transmission still makes sense [3]; in particular this is thecase for a Bosonic Gaussian q-c channels where we also demonstrated the gainof entanglement assistance.

On the contrary, as shown in [5], finite dimensional c-q channels (prepara-tions) are essentially characterized by the property of having no gain of entan-glement assistance. In a sense preparations are “more classical” than measure-ments, being not sensible to the entanglement assistance. In [4] we introduceand study Bosonic Gaussian c-q channels; we observe that the embedding of theclassical input into quantum is always possible and Cea under appropriate inputconstraint is thus well defined. We establish a property of entropy increase forthe channel environment, that implies equality C = Cea at least for a mini-mum noise Gaussian c-q channel under special input constraint. On the otherhand, we argue that under generic input constraint, the gain of entanglementassistance Cea/C > 1 holds also for classical-quantum channels.

Acknowledgment: This work was partly supported by RFBR grant N 12-01-00319-a, Fundamental Research Programs of RAS and the Russian QuantumCenter.

References

[1] C.H. Bennett, P.W. Shor, J.A.Smolin, A.V.Thapliyal, “Entanglement-assisted classical capacity of noisy quantum channel,” Phys. Rev. Lett.83, 3081-3084 (1999); arXiv:quant-ph/9904023.

[2] A.S. Holevo, Quantum systems, channels, information (Berlin/Boston, De-Gruyter, 2012).

[3] A.S. Holevo, “Information capacity of quantum observable,”arXiv:1103.2615 [quant-ph].

[4] A.S. Holevo, “Gaussian classical-quantum channels: gain of entanglement-assistance,” arXiv:1211.4774 [quant-ph].

[5] M.E. Shirokov, “Conditions for equality between entanglement-assistedand unassisted classical capacities of a quantum channel,” arXiv:1105.1040[quant-ph].

2

Making a large entangled state from a small one

A. I. Lvovsky1,2,*

, A. S. Prasad1, R. Ghobadi

1,

A. Chandra1, C. Simon

1, Y. Kurochkin

1,2

2Russian Quantum Center, 100 Novaya St., Skolkovo,Moscow 143025, Russia

1Institute for Quantum Information Science, University of Calgary, Calgary, Canada, T2N 1N4

*[email protected]

Abstract: We present two experiments on manipulating optical entanglement. In the first one, we

generate a micro-macro entangled state from a microscopic one. In the second, we enhance the

entanglement of the Einstein-Podolsky-Rosen state.

The technology of preparing entangled optical states and enhancing their entanglement is of key importance for

applications in quantum information technology, such as quantum communication, metrology and computation.

Here we demonstrate two separate experiments on manipulating optical entanglement.

Our first experiment relates to famous Schrodinger’s cat, in which a microscopic entity becomes entangled with a

macroscopic one. Here we demonstrate conclusively for the first time the creation of micro-macro entanglement

in light. The macro system involves over a hundred million photons, while the micro system is at the single-

photon level. We show that microscopic differences (in field quadrature measurements) on one side are correlated

with macroscopic differences (in the photon number variance) on the other side. We demonstrate entanglement of

our state by bringing the macroscopic state back to the single-photon level and performing full quantum state

tomography of the final state.

In our second experiment we demonstrate an efficient experimental technique to enhance continuous variable

entanglement of a two mode squeezed state. We apply photon annihilation operator to both modes of a two mode

squeezed state generated by Type-II spontaneous parametric down-conversion. The annihilation operator is

implemented using a polarization independent asymmetric beam splitter. Conditioned on simultaneous ‘clicks’

heralding successful photon annihilation, we employ homodyne tomography to reconstruct the resulting two mode

state and verify entanglement distillation.

Quantum gates with mesoscopic atomic ensembles

I. I. Beterov,1, 2

, M. Saffman,3 E. A. Yakshina,

1, 2 V. P. Zhukov,

4 D. B. Tretyakov,

1 V. M. Entin,

1

I. I. Ryabtsev,1, 2, 5

C. W. Mansell,6 C. MacCormick,

6 S. Bergamini,

6 and M. P. Fedoruk

2

1A.V.Rzhanov Institute of Semiconductor Physics SB RAS, 630090 Novosibirsk, Russia 2Novosibirsk State University, 630090 Novosibirsk, Russia

3Department of Physics, University of Wisconsin, Madison, Wisconsin, 53706, USA 4Institute of Computational Technologies SB RAS, 630090 Novosibirsk, Russia

5Russian Quantum Center, Skolkovo, Moscow Reg., 143025, Russia 6The Open University, Walton Hall, MK7 6AA, Milton Keynes, UK

Quantum information can be stored in collective states of ensembles of strongly

interacting atoms [1]. This idea can be extended to encoding an entire register of qubits in

ensembles of atoms with multiple ground states which opens up the possibility of large quantum

registers in a single atomic ensemble or of coupling arrays of small ensembles in a scalable atom

chip based architecture. Our proposal for implementing high fidelity quantum gates in ensembles

is thus of interest for several different implementations of quantum computing.

The enhanced coupling of the mesoscopic ensembles to the radiation field by a factor of

N , with N the number of atoms, is useful for coupling matter qubits to single photons.

However, due to the increase of the Rabi frequency of oscillations between different collective

states proportional to N , with the one atom Rabi frequency, it is difficult to perform gates with

well defined rotation angles in the situation where N is unknown [2]. Adiabatic passage

techniques have been widely used for deterministic population transfer in atomic and molecular

systems [2,3]. Although STIRAP or Adiabatic Rapid Passage (ARP) methods provide pulse

areas with strongly suppressed sensitivity to the Rabi frequency N, and therefore suppressed

sensitivity to N, the phase of the final state is in general still strongly dependent on N.

In this work we propose double adiabatic sequences using either STIRAP or ARP

excitation which remove the phase sensitivity, and can be used to implement gates on

collectively encoded qubits without precise knowledge of N. Our approach is shown in Fig. 1. A

sequence of two STIRAP pulses is produced with fields having Rabi frequencies 2,1 , and

detuning from the intermediate state. A Rydberg state r is excited by a counterintuitive

sequence of laser pulses in the regime of Rydberg blockade, where excitation of more than one

Rydberg atom is suppressed due to strong dipole-dipole interaction between the atoms [1]. The

second reverse STIRAP sequence, as shown in Fig. 1(a), returns the Rydberg atom back to the

ground state. As we have shown in our recent work [2], large detuning from the intermediate

excited state e is required for deterministic single-atom excitation after the first STIRAP

sequence, which is represented by the

solid curve in Fig. 1(d). Deterministic

single-atom excitation can also be

achieved using linearly chirped ARP

pulses, as shown in Figs. 1(c),(d).

At the end of a double STIRAP sequence

the population is returned back to the

collective ground state 0000 of the

atomic ensemble, but a geometric phase is

accumulated. This phase shift of the

ground state is dependent on the Rabi

frequency and leads to gate errors. The

phase of the atomic wavefunction can be

compensated by switching the sign of the

Figure 1 (a) Energy levels for two-photon STIRAP

and single-photon ARP excitation; (b) Time sequence

of STIRAP laser pulses; (c) Time sequence for ARP laser

excitation;

(d) Time dependence of the single-atom excitation probability.

2

1

(a)

0

1

r

e

t

0

r

STIRAP

ARP

detuning between two STIRAP sequences,

or by switching the phase between two

ARP pulses, as shown in Fig. 1(c). For a

double STIRAP sequence with the same

detuning throughout the accumulated

phase depends on N [Fig.2(a)], while the

phase change is zero, independent of N,

when we switch the sign of detuning

between the two STIRAP sequences [Fig.

2(b)]. A similar phase cancellation occurs

for phase shifted ARP pulses [Fig. 2(c)].

The phase compensated double

STIRAP or ARP sequences can be used to

implement a universal set of quantum

gates as we now describe. Consider atoms

with levels re ,,1,0 as shown in Fig.

1. A qubit can be encoded in an N atom

ensemble with the logical states

000000 ,N

j jN 101..0

11 .

Levels 1,0 are atomic hyperfine ground

states with coupling between these states

and implementation of quantum gates

mediated by the singly excited Rydberg

stateN

j jrN

r1

0..01

. Single-

qubit rotations are implemented using

transitions between Rydberg states

10 rr , driven by microwave

radiation, as shown in Fig.2(d). Single-

atom addressability is necessary when the

atoms are excited into the Rydberg states.

The scheme of CNOT gate, shown in

Fig.2(e), is an extension of the method implemented in Ref.[4].

We have analyzed double STIRAP and ARP sequences with phase compensation for

quantum gates in collectively encoded ensembles. Our analysis shows that high fidelity universal

gates can be achieved using available experimental resources. We have made explicit

calculations for N = 1..10 showing the performance of these pulse schemes. For larger

ensembles, with smaller fractional variation in N, the performance will be even better. We

anticipate that these ideas will contribute to realization of quantum logic using collectively

encoded qubits and registers.

This work was supported by the grant of the President of Russian Federation MK.7060.2012.2,

EPSRC project 5EP/K022938/1, RFBR (Grant No.13-02-00283) RAS and SB RAS. MS was

supported by the NSF and the AFOSR MURI program.

[1] M. D. Lukin et a., Phys. Rev. Lett. 87, 037901 (2001).

[2] I. I. Beterov et al., Phys. Rev. A 84, 023413 (2011).

[3] I. I. Beterov et al, arXiv:1212.1138

[4] L. Isenhower et al, Phys. Rev. Lett. 104, 010503 (2010).

-2

0

2

-2

0

2

-8 -6 -4 -2 0 2 4 6 8

-2

0

2

-8 -6 -4 -2 0 2 4 6 8 -8 -6 -4 -2 0 2 4 6 8

N=1

t (�s)t (�s)

N=1 N=1

(b) STIRAP��/2��=200 MHz�sign(t)

N=2 N=2 N=2

N=7

(c) ARP(a) STIRAP��/2��=200 MHz

N=7 N=7

t (�s)

Phase

of

wave

funct

ion

0

0r

1r

�

N� � �

� � ,R

�

N�

2 43

1 5

0

11

0r

1r

�

CN

� �

tN

��

tN

��

CN

�

� �

� �

4 4

control target

2 37 5 61(d) (e)

Figure 2. Calculated time dependence of the phase of the

collective ground state amplitude for N =1, 2, 7 atoms (top to

bottom). Double STIRAP sequence with 2/ = 200 MHz

(a), with 2/ = 200 MHz ×sign (t) (b), and for a double

ARP pulse sequence with phase inversion (c). All other

parameters are as in Fig. 2. (e) Single qubit gate for a

mesoscopic qubit with N atoms. Pulses 1 5 act between the

qubit states | 1,0 and the Rydberg states 10 , rr . Pulses

1, 2, 4, 5 are optical transitions and pulse 3 is a microwave

frequency transition between Rydberg states. (b) CNOT gate

between mesoscopic qubits with Nc atoms in the control qubit

and Nt atoms in the target qubit.

DEVELOPMENT OF DEEP UV CONTACT

LITHOGRAPHY FOR FABRICATION OF POLYMER

WAVEGUIDE ARRAYS WITH HIGH INTEGRATION

LEVEL ON THE PRINTED CIRCUIT BOARD

K.V. Khaydukov1,2

, A.S. Akhmanov1, V.Ya. Panchenko

1, A.G. Savelyev

1, V.I. Sokolov

1, E.V. Khaydukov

1

1Institute on laser and information technologies of the Russian academy of sciences

140700, Shatura, Moscow reg., Sviatoozerskaya str. 1, Russia 2Volgograd State University

400062, Volgograd, Universitetsky Ave., 100, Russia

e-mail: [email protected]

The method of deep UV contact lithography for fabrication of polymer integrated optics waveguides arrays on the

printed circuit board is developed. The method permits to fabricate both multimode and single-mode polymer

waveguides with high aspect ration and high integration level directly from the fluorine - containing liquid

compositions, having low absorption losses in 0.85, 1.3 and 1.55 m telecom wavelength regions.

The arrays of polymer waveguides are fabricated on the standard FR4 printed circuit board by using fluorinated

acrylic monomers. We employed UV light with the wavelength of actinic radiation in the range from 240 up to 280

nm to fabricate the waveguides. The integration level of the waveguides in the array equals 625 pcs/cm, Fig. 1. This

exceeds the integration level of the waveguides in the optical bus presented by IBM Inc. and known as «Green

Optical Link».

Fig. 1. (a) Photograph of the

array of the multimode

polymer waveguides on the

printed circuit board FR4.

Top view (a), butt view (b).

The fabricated arrays of polymer waveguides on PCB can be used as a high-speed optical bus for micro-processor

computing systems.

The research is supported by grant of RFBR 12-07-31223 _ and grant of the President of Russian Federation

for the state support of young Russian scientists -6798.2013.9.

Generation Of High-Frequency Entangled CV States By

Coupled Parametric Optical Interactions

M.Yu. SayginGeneral Physics and Wave Processes Department, Faculty of Physics, M.V. Lomonosov Moscow State University; International Laser

Center, M.V. Lomonosov Moscow State UniversityLeninskie Gory, Moscow 119992, Russia;

FAX: +7 495/939-3113; e-mail: [email protected]

Abstract: We theoretically study the formation of high-frequency entangled continuous variable

states, generated in a multifrequency parametric optical process, comprised of three three-wave

processes with shared frequencies.

Introduction

Entangled states play important role in quantum information due to their unique properties, having

no counterparts in classical physics. In the talk I’ll be reporting the results on the study of the

entanglement properties of optical fields of continuous variable [1], generated in coupled parametric

interactions. The interactions under investigation are the following three three-frequency parametric

processes:

42

31

21

,

,

P

P

P

(1)

where l is the carrier frequency (for 4,...,1l ) and P is the pumping frequency. The processes

(1) can evolve simultaneously in a single nonlinear crystal [2].

The approach used

It has been shown previously, that the two-frequency entanglement is formed between the down-

converted modes and the up-converted ones as well [3]. It has also been shown that the parametric

amplification at low-frequency can be realized in (1) [4].

In the present report we analyze the CV states, obtained in (1), by exploitation of the singular

value decomposition (SVD) tool. SVD is a particularly insightful approach to study multipartite

states, produced by Hamiltinians of the second-order with respect to the creation/annihilation

operators. Such Hamiltonians lead to the following simple form of the operator evolution:

),ˆˆ(ˆ4

1jljljljl aBaAb (2)

where is the annihilation (creation) photon operator of the corresponding carrier frequency

( ), and are the transformation coefficients, which are dependent on the parameters

of the system under consideration. According to SVD the matrices

)ˆ(ˆ jj aa

4,..., A1j jl jlB

A and B , comprised of the

transformation coefficients from (2), can be expanded to get the form:

VUAA D (3) TDVUBB

where matrices U and V are the linear transformations, realized by multiport interferometers, while

and are the squeezing transformations. DA DB

Results

The explicit form of the linear (matrices U and V ) and squeezing transformations ( and )

have been found (see. Fig. 1, where the case of equal up-conversion efficiency is presented). The

dependence of the squeezing parameters and the beam-splitter parameters on the parameter of the

parametric multifrequency system have been found and analyzed. It has been found, that at the

traveling wave regime, the amount of squeezing at the up-converted modes is smaller, then that of the

down-converted modes. We describe possible ways to overcome with limitations and the intracavity

configuration has been suggested.

DA DB

Fig. 1 Schematic of the singular value decomposition, corresponding to (1) for the case with equal

up-conversion efficiencies. Here, the beam-splitter transformations combine optical modes of

different carrier frequencies, that can be realized by means of up-conversion processes.

Two advantages of the coupled interactions (1) are to be mentioned. Firstly, the exploitation of the

up-converted optical modes enables generation of two-mode entanglement from the high-frequency

spectral domain, which is a problem for single PDC processes, since the pumping can fall into the

absorption band of the crystal. Secondly, besides the two-frequency entanglement, the four-frequency

entanglement is present: the block of down-converted modes is entangled with the up-converted

modes block. This can find applications in quantum information schemes requiring the interface

between low-frequency and high-frequency optical spectrum domains.

References

[1] S.L. Braunstein, P. van Loock, Quantum information with continuous variables, Rev. Mod. Phys. 77, p. 513-

577 (2005).

[2] A.S. Chirkin, I.V. Shutov, On the possibility of the nondegenerate parametric amplification of optical waves

at low-frequency pumping, JETP Lett. 86, 11, p.803-807 (2007) (translated from Russian).

[3] M.Yu. Saygin, A.S. Chirkin, M.I. Kolobov, Quantum holographic teleportation of entangled two-color

optical images, JOSA B 29, 8, p. 2090-2098 (2012).

[4] M.Yu. Saygin, A.S. Chirkin, Simultaneous parametric generation and up-conversion of entangled optical

images. Journal of Experimental and Theoretical Physics 111, 1, p. 11-21 (2010) (translated from Russian).

[5] S.L. Braunstein, Squeezing as an irreducible resource, Phys. Rev. A 71, 055801 (2005).

Intrinsic defects in silicon carbide for spin-based quantum applications

V. Dyakonov1,3

, D. Riedel1, V. A. Soltamov

2, F. Fuchs

1, H. Kraus

1, S. Väth

1, A. Sperlich

1, P.

G. Baranov2, G. V. Astakhov

1

1Experimental Physics VI, University of Würzburg, 97074 Würzburg, Germany2Ioffe Physical-Technical Institute, 194021 St. Petersburg, Russia

3Bavarian Center for Applied Energy Research, 97074 Würzburg, GermanyE-mail: [email protected]

We present a number of experiments that demonstrates a high potential of atomic-scale

defects in silicon carbide (SiC) for various spin-based applications, including quantum

information processing and photonics.

In particular, we show that defect spin qubits in SiC can be addressed, manipulated and

selectively read out by means of the so-called double radio-optical resonance [1]. The

situation reminds the one in the atomic spectroscopy, where the atoms have their individual

extremely sharp optical and radiofrequency resonance fingerprints. Furthermore, from the

transient spin resonance experiments we deduce reasonably long spin memory, in the range of

hundred microseconds.

We also generate inverse population in some intrinsic defects, resulting in stimulated

microwave emission at room temperature. This is a crucial step towards implementation of

highly-integrable solid-state masers and extraordinarily sensitive microwave detectors. All the

above-mentioned observations are due to the unique spin properties of the silicon vacancy-

related defects in SiC. We are able to identify several defects of this type and ascertain their

crystallographic structure. Taking into account the polymorphism of SiC, there is a multitude

of such intrinsic defects with highly individual quantum properties in this technologically

advanced material.

As an application example, we incorporate intrinsic defects in LED structures and show

that they can be electrically driven at room temperature [2]. Provided some of these defects

emit in near infrared, our approach opens a new avenue for the fabrication of cheap and robust

single photon sources for quantum telecommunications. On the other hand, we observe two-

quantum microwave emission, which can potentially be used to generate entangled photon

pairs. This may lead to a new platform for quantum electrodynamics experiments and

quantum information processing at room temperature, with all elements being integrated on a

single chip.

References:

[1] D. Riedel et al., Phys. Rev. Lett. 109, 226402 (2012), arXiv:1210.0505.

[2] F. Fuchs et al., arXiv:1212.2989.

Response of Photoreceptor Cells to Single- and Multi- Photon Stimulation

Mai Phan1, Mei Fun Cheng1, Dmitri Bessarab2, and Leonid Krivitsky1

1 Data Storage Institute, Agency for Science Technology and Research, 117608 Singapore

2Institute of Medical Biology, Agency for Science Technology and Research, 138648 Singapore [email protected]

We study responses of retinal photoreceptors (retinal rods) to stimulation by precisely controlled light pulses at a single photon level. The single photon pulses are generated via a

process of spontaneous parametric down conversion.

This study is motivated by the ultimate sensitivity of animal retinal rods to light stimulation and by the ability to precisely control single photon pulses, accessible through quantum optics experiments. The fusion of these ideas opens a new interdisciplinary application of quantum optics in biology.

Single photon stimuli are produced via a process of Parametric Down Conversion in which a fraction of a laser pulse, propagating in a non-linear crystal, is converted into a pair of photons (signal and idler), obeying conservation of energy and momentum. Since signal and idler photons are emitted only in pairs, if an idler photon is absorbed into a rod cell it is be possible to capture a true single photon stimulation response which should be correlated with the measurements of a signal photon. The single photons are delivered to the cell via an optical fiber [1].

Readout from the cell is recorded with a low-noise electrophysiology patch-clamp setup that allows recording of an amplified photo-induced current through a rod membrane and capture of its alteration upon absorption of a photon. Retinal rod cells are isolated from adult frog Xenopus laevis.

The results contribute to a better understanding of fundamental properties of visual pathways in living species [2]. The practical applications include absolute calibration of quantum efficiency of a cell, study of multi-photon responses, and possible development of a light bio-sensor.

1. N.Sim, D. Bessarab, M. laser beam to isolated retinal rods by fiber optics Biomedical Optics Express, 2 , 2926-2933 (2011).

2. N.Sim, D. Bessarab, M. asurement of photon statistics with live photoreceptor cells , 109, 113601 (2012).

Single-Qubit Laser – A Source of Non-Classical Light

for Quantum Information Applications

Sergei Ya. Kilin, Alexander B. MikhalychevB.I. Stepanov Institute of Physics, NAS of Belarus, Nezavisimosti ave., 68, Minsk, Belarus

[email protected]: We provide general unique and uniformly applicable solution for single-qubit

laser stationary state in terms of nonlinear coherent states, prove non-classicality of the state

and introduce nonlinear transition probabilities, revealing quantum nature of single-qubit

laser.

1. Introduction

The one-atom-one-mode microlaser is of a great importance as a limiting case of lasers. This intrinsically

quantum system with a number of properties strongly different from ordinary lasers requires specific cavity

quantum electrodynamics methods for its description [1]. Rabi splitting [2], collapse-and-revival phenomenon

[3] and photon blockade effect [4] are a few examples of quantum effects observed in the system.

Contrary to conventional lasers, microlasers (and especially single-atom lasers) are known to be sources of

non-classical light [5, 6]. It has already been shown, that single-atom laser, considered within the scope of

strong-coupling regime, can produce special kind of nonlinear coherent states (NCSs), namely Mittag-Leffler

coherent states [7]. In this contribution we provide general uniformly applicable description of single-atom laser

and show that it generates NCSs for any values of interaction parameters [8].

Also we show that intrinsic quantum character of light-matter interaction in single-atom laser reveals itself

as impossibility of describing the lasing effect by means of field-independent spontaneous and induced

transition probabilities as in the case of a conventional laser. The effect has been mentioned for strong-coupling

regime in Ref. [7]. Here we show that this property is general and is preserved beyond strong-coupling regime.

To characterize stationary state non-classicality quantitively, as well as to provide classification of present

non-classicality types, we consider non-classicality parameters [9], based on s-parametrized phase space

functions [10, 11] P( ; s). This consideration reveals state non-classicality, not described correctly by either

strong-coupling or semi-classical approximations, and proves that single-qubit laser is an important source of

non-classical states for all regimes of operation, including self-quenching and thermal ones. Phase space

functions also represent a useful tool for describing dynamics of single-qubit laser and changes of non-

classicality types in the system approaching its stationary state. Three regimes (coherent, incoherent and

stationary state approaching) of dynamics can be introduced on the basis of such consideration.

2. Stationary state as a phase-averaged nonlinear coherent state

We consider the following model of a single-qubit laser. A 2-level system with the ground state 1 and excited

state 2 interacts with a resonance field mode with coupling constant g. The qubit is pumped incoherently with

mean rate R12. Decay of the resonance field mode and decay and dephasing of the qubit with rates , R21 and

correspondingly are taken into account. The master equation for the density matrix, reduced over the states of

the surrounding, in interaction representation has the form:

12 21, 2 ,za

i H L R L R L L

where operators , , z and a†, a describe dynamics of atom and field correspondingly, and relaxation is

described by Lindblad operators: † † †2 2XL X X X X X X . The atom-field interaction is described by

Jaynes-Cummings Hamiltonian †( )H g a a .

The state of the system is completely described by operators 11

1 1 ,22

2 2 and †1 2u i a .

In the stationary state the operators are diagonal in Fock states basis and can be expressed on the basis of

eigenvalues of a deformed annihilation operators. For example, one can show that the conditional density matrix

11 satisfies the following equation: 11 11

† 2

11 0 11F FA A a , where 2

0 12 / (4 )a R is normalized pump rate;

†( ) FA F aa a is deformed annihilation operator [12, 13] with the properties completely determined by

discrete function F(n) (deformation function). For the ground-state conditional density operator this function

equals 11 0(1 / 2) (1/ 2 /) ( ) {1 }F n n d n , where 0 21( 2 ) / (4 )R describes atomic loss excess

over field loss and d(n) is a function, characterizing deviation of the density matrix from strong-coupling regime

(see Ref.[8] for details). Eigenstates of deformed annihilation operators are known as nonlinear coherent states

[12, 13] and represent a particular case of generalized coherent states (see e.g. [14]). In the special case 0 0 ,

0d n eigenstates of operator A are ordinary coherent states. For 0 0 , 0d n (strong-coupling regime)

the eigenstatates are Mittag-Leffler states [7].

3. Nonlinear transition probabilities

The existing connection between the conditional density operators 11 and 22 in the stationary state can be

interpreted as balance of transitions between states with different photon numbers:

22 11 22 111 { ( 1)} 2 ( 1){ 1 ( 1)},nn w n n n n nwhere left-hand side describes field-induced transitions between ground and excited states of the atom, right-

hand side corresponds to mode decay. The normalized transition probability wn is approximately constant for 2

0 0 /n a (Fig. 1(1)), as it should be for ordinary spontaneous and induced transitions. However, for

large photon numbers n it becomes strongly intensity-dependent: 2 ~ / ( )nw g n , and decreases with growth of

n in such a way that the total transition probability (n+1)wn tends to a constant value: 21 /nn w g .The

found “saturation” of a single-atom laser is a manifestation of its quantumness, revealing itself in an extremely

strong correlation of atom and field states (compared to conventional laser) and leading to invalidity of mean-

field and other semi-classical approaches.

4. Quasi-distributions, non-classicality order and system dynamics

One can show that any classical state is characterized by positive quasi-distribution functions P( ; s) for

1 1s . On the other hand, positivity of P( ; s) for all s in the considered interval implies non-negativity of

the Glauber function and, therefore, classicality of the state. Thus, minimal value s0 for which the function P( ;

s) becomes negative characterizes the “order” of state non-classicality. Calculation of this value for the

stationary state of single-qubit laser proves the state non-classicality for any interaction parameters and all

regimes of operation (Fig. 1(2-3)).

(1) (2) (3)

Fig. 1. (1) Normalized total effective transition probability: solid lines – numerical calculation, dashed line – approximate analytical

expression valid for large n, dash-dotted lines – “classical” transition probability. Black lines: 0 1 , 2

0 1a , ; grey lines: 0 5 ,

2

0 5a , 190 (strong dephasing regime – semi-classical behavior). (2) Stationary state non-classicality order (black lines) and

correlation function (gray lines). Parameters: 0

1 (solid line), 0 (dashed line), -0.5 (dot-dashed line); 0 . Regions of sigle-qubit laser

operation [15]: (a) — linear, (b) — quantum nonlinear, (c) — lasing, (d) — self-quenching, (e) — thermal. Inequality s0 < 1 (state non-

classicality criterion) holds for all the regimes, including the ones with g(2) > 1. (3) Dynamics of non-classicality order: 2

0 1a , 0 1 (solid

line), 2

0 1a , 0 0.3 (dashed line), 2

0 0.1a , 0 0.3 (dot-dashed line). Regimes of dynamics: (a) – coherent, (b) – incoherent, (c) –

approaching stationary state.

[1] P. R. Berman, Cavity Quantum Electrodynamics, Academic Press, 1994.

[2] R. J. Thompson, G. Rempe, and H. J. Kimble, “Observation of normal-mode splitting for an atom in an optical cavity,” Phys. Rev.

Lett. 68, 1132 (1992).

[3] J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum

model,” Phys. Rev. Lett. 44, 1323 (1980).

[4] K. M. Birnbaum, A. Boca, R. Miller, et al., “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87 (2005).

[5] J. McKeever, A. Boca, A. D. Boozer, et al., “Deterministic generation of single photons from one atom trapped in a cavity,”

Science 303, 1992 (2004).

[6] T. Wilk, S. C. Webster, A. Kuhn, et al., “Single-atom single-photon quantum interface,” Science 317, 488 (2007).

[7] S.Ya. Kilin and T. B. Karlovich, “Single-atom laser: coherent and nonclassical effects in the regime of a strong atom-field

correlation,” JETP 95, 805 (2002).

[8] S. Ya. Kilin and A. B. Mikhalychev, “Single-atom laser generates nonlinear coherent states,” Phys. Rev. A 85, 063817 (2012).

[9] N. Lutkenhaus and S. M. Barnett, “Nonclassical effects in phase space,” Phys. Rev. A 51, 3340 (1995).

[10] K. E. Cahill and R. J. Glauber, “Ordered expansions in boson amplitude operators,” Phys. Rev. 177, 1857 (1969).

[11] G.S. Agarwal and E. Wolf, “Ordering theorems and generalized phase space distributions,” Phys. Lett. A 26, 485 (1968).

[12] R. L. de Matos Filho and W. Vogel, “Nonlinear coherent states,” Phys. Rev. A 54, 4560 (1996).

[13] V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, “f-oscillators and nonlinear coherent states,” Phys. Scr. 55, 528

(1997).

[14] A. Perelomov, Generalized Coherent States and their Applications, Springer-Verlag, 1986.

[15] E. delValle and F.P. Laussy, “Regimes of strong light-matter coupling under incoherent excitation,” Phys. Rev. A 84, 043816

(2011).

Experimental demonstration of a dimensionwitness of classical and quantum systems

Martin Hendrych1, Rodrigo Gallego1, Michal Micuda1,2, Nicolas Brunner3,

Antonio Acin1,4 and Juan P. Torres1,5

1 ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, Av. Carl Friedrich Gauss 3, 08860,Castelldefels, Barcelona, Spain

2 Department of Optics, Palacky University, 17. listopadu 12, 77146 Olomouc, Czech Republic3 H.H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, United Kingdom

4 ICREA-Institucio Catalana de Recerca i Estudis Avancats, 08010 Barcelona, Spain5 Department of Signal and Theory and Communications, Universitat Politecnica de Catalunya, Jordi Girona 3,

08034 barcelona, [email protected], [email protected]

Abstract: We report on the experimental demonstration of dimension witnesses ina prepare and measure scenario. For this, we make use of hyper-entangled photonpairs to generate ensembles of classical and quantum states.

OCIS codes:One of the principle tenets on which the description of a physical system is based is its dimensionality, thatis, the number of relevant and independent degrees of freedom needed to describe it. A natural questionis whether the dimension of an unknown system, classical or quantum, can be estimated experimentally.The concept of a dimension witness allows one to establish lower bounds on the dimension of an unknownsystem in a device independent way, that is, only from the collected measurement statistics, without makingany assumption about the detailed functioning of the devices used in the experiment.

Recently, a general framework for the study of this question has been proposed [1]. In this approach,dimension witnesses are defined in a prepare and measure scenario where an unknown system is subjectto different preparations and measurements. One of the advantages of this approach is its simplicity froman experimental viewpoint when compared with previous proposals. In our experiment we focus on adimension witness (I4) for a scenario consisting of x= 1...4 possible preparations and y= 1...3 measurementswith only two possible outcomes, labeled by b =±1. For further details, please see [1].

Here we demonstrate experimentally such a dimension witness [2]. The set-up (see Fig. 1) consists oftwo devices, the state preparator and the measurement device. The state preparator consists of a source ofentangled photons (A), followed by a measurement (B) on one photon of the pair (idler) that prepares itstwin photon (signal) in the desired state. The signal photon is then sent to the measurement device. Block(A) is the source of entangled photons. The second harmonic (Inspire Blue, Spectra Physics/Radiantis) at awavelength of 405 nm of a Ti:sapphire laser in the picosecond regime (Mira, Coherent) is shaped by a spatialfilter (SF) and focused into a 1.5 mm thick crystal of beta-barium borate, where spontaneous parametricdown-conversion takes place. The nonlinear crystal (XL) is cut for collinear type-II down-conversion sothat the generated photons have orthogonal polarizations.

&

SLMPBSm=+1

PBS

H+V|

H V| |m= 1|

V|

H|

(1) (2) (3)

MEASUREMENT

DEVICE

STATE

PREPARATOR

QUBIT: QUTRIT: QUART:

| = cos |H,+1 + sin |V,+1�

��

��

| = cos |H,+1 - sin |V,+12

� ��

��

| = |H,+13

�

| = |V,+14

�

| = cos |H,+1 + sin |V,+11

� ��

��

| = cos |H,+1 - sin |V,+12

� ��

��

| = |H,-13

�

| = |V,+14

�

| = |H,+11

�

| = |H,-12

�

| = |V,+13

�

| = |V,-14

�

yx(I)

(II) (III)

b

SIGNAL

IDL

ER

FDLXLSF L

(A)

SLMP SMF DFLH PW

SLM P

BS

SMFD FL H PW(B)

(B)

M

M

Fig. 1. Experimental set-up.

Fig. 2. Experimental results

We exploit the angular momentum of the down-converted photons [3], which contains a spin contri-bution associated with the polarization, and an orbital contribution associated with the spatial shape ofthe light intensity and its phase. Within the paraxial regime, both contributions can be measured and ma-nipulated independently. The polarization of photons is represented by a two-dimensional Hilbert space,spanned by two orthogonal polarization states (for example, horizontal and vertical). The spatial degreeof freedom of light lives in an infinite-dimensional Hilbert space, spanned by paraxial Laguerre-Gaussianmodes. Laguerre-Gaussian beams carry a well-defined orbital angular momentum (OAM) of mh (m is aninteger) per photon that is associated with their spiral wavefronts.

Before splitting the signal and idler photon, a polarization-dependent temporal delay τ is introduced. Thedelay line (DL) consists of two quartz prisms whose mutual position determines the difference between thepropagation times of photons with orthogonal polarizations. The delay line is used to implement a contin-uous transition from quantum to classical states. If the temporal delay between the photons exceeds theircorrelation time, the coherence is lost; that is, the off-diagonal terms vanish for all states in the ensemble.

Block (B) performs a measurement on the idler photon to prepare the signal photon. It consists of ahalf-wave plate (HWP), polarizer (P), spatial-light modulator (SLM) and a Fourier-transform lens (FL). Thehalf-wave plate and polarizer project the photon into the desired polarization state. The desired OAM stateis selected by the SLM. SLM encodes computer-generated holograms that transform the m = +1 state orm = −1 state into the fundamental LaguerreGaussian state LG00 that is coupled into a single-mode fibre(SMF). The measurement device uses an identical block (B) to measure the signal photon.

Ensembles of quantum states are prepared in the experiment (II in Fig. 1) to generate classical and quan-tum states of dimension 2 (bits and qubits, respectively), classical and quantum states of dimension 3 (tritsand qutrits), and classical states of dimension 4 (quarts). Finally, several measurements (III in Fig. 1) areperformed at the measurement device for qubits and qutrits. In the case of quarts, the three measurementsare constructed by combining (1) and (2).

Experimental results are shown in Fig. 2. The solid lines indicate the maximum value of I4 that a givensystem of dimension d can attain. For instance, two-dimensional systems (d = 2, bits and qubits) can neverreach values I4 > 6, while classical two-dimensional systems (bits) can never attain I4 > 5. Three-dimensional(d = 3, trits and qutrits) systems can never fulfill I4 > 7.97, while classical three-dimensional systems (trits)are restricted to I4 < 7.

References

[1] R. Gallego, N. Brunner, C. Hadley, and A. Acin, “Device-independent tests of classical and quantum dimensions,” Phys. Rev. Lett.105, 230501 (2010).

[2] M. Hendrych, R. Gallego, M. Micuda, N. Brunner, A. Acin and J. P. Torres, and L. Torner, “Experimental estimation of the dimen-sion of classical and quantum systems,” Nature Phys. 5, 588 (2012).

[3] G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature Phys. 3, 305 (2007).

Guided-wave-coupled nitrogen vacancies in nanodiamond-doped

photonic-crystal fibers

I. V. Fedotov1,2

,N. A. Safronov1

Yu. A. Shandarov1

, A. A. Lanin1

, A. B. Fedotov1,2

, S. Ya. Kilin3

,�A.P. Nizovtsev3

, V.N.

Chizevski3

, D.I. Pustakhod3

, and A. M. Zheltikov1,2,4

1) Physics Department, Russian Quantum Center, International Laser Center, M.V. Lomonosov Moscow State University, Moscow 119992, Russia

2)�Department of Neuroscience, Kurchatov National Research Center, Moscow, Russia

3)B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus

4) Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA

Abstract: Zero-phonon-line (ZPL) emission of nitrogen vacancies (NVs) is coupled to the guided modes of

solid- and hollow-core nanodiamond-doped photonic-crystal fibers (PCFs). Both types of PCFs are tailored

toward enhancing ZPL emission coupling to the fiber modes.

The unique photophysics of nitrogen vacancies (NVs) in diamond is at the heart of rapidly growing diamond photonics,

giving a powerful momentum to quantum information technologies, [1–3] bioimaging, [3,4] and nanoscale magтetic sensing.

[5,6] The NV centers in diamond offer much promise for the creation of robust and reliable single-photon sources, opening

new horizons in quantum computations, quantum communications, and single-photon spectroscopy. The low photon

outcoupling efficiency typical of NV centers in a bulk crystal and the necessity to connect NV centers into large-scale quantum

information networks and distributed quantum computers call for the strategies that would allow NV centers to be coupled to

optical waveguides. Several attractive and elegant solutions to this problem have been recently demonstrated, including

fabrication of NV-center-embedded diamond nanowires, [7] placing diamond nanoparticles on a facet of a photonic-crystal

fiber (PCF), [8] coupling NV diamond centers to a semiconductor waveguide, [9] and doping solid-core PCFs with NV

diamond nanoparticles. [10]

Here, we report a direct coupling of the zero-phonon- line (ZPL) NV emission to the guided modes of solid- and hollow-

core nanodiamond-doped PCFs. We demonstrate that both types of PCFs can be tailored toward enhancing ZPL emission

coupling to the fiber modes using the evanescent field of waveguide modes in ultrasmall-silica-core PCFs and air-core-guided

modes in hollow PCFs. Both PCF designs are shown to facilitate the detection of ZPL photons from low densities of diamond

NV centers against the Raman background from the fiber.

Figure 1. Coupling nitrogen vacancies to waveguide modes of a nanodiamond-doped solid-core (a) and hollow-core (b) photonic crystal fiber.

In our experiments, the PCFs were infiltrated [10,11] with a syringe-pressurized fluid (water or ethanol) containing NV-

diamond nanoparticles with a mean diameter of 300 nm. The liquid carrying the diamond nanoparticles was then dried out,

with the NV-center nanodiamond left deposited on the walls of the air holes. The 532-nm, 100-mW second-harmonic output of

a diode-pumped continuous-wave Nd:YAG laser coupled into the PCF was used as a source of optical pump. The

photoluminescent response of the NV centers inside the fiber was analyzed with a standard spectrometer. In the PCF of the first

type (Fig. 1(a)), 532-nm pump radiation guided along a small silica core of the fiber provides excitation of the NV diamond

centers with its evanescent field. The fiber core diameter for this type of nanodiamond-doped waveguide structure is chosen as

a compromise between the energy of the evanescent field, which is controlled by the fraction of the mode energy carried by the

evanescent-field tails outside the fiber core, and the waveguide and beam-incoupling losses, which tend to dramatically

a) b)

increase with a decrease in the fiber core diameter. For PCFs doped with relatively high densities of NV centers (higher than

104

per 1 cm of PCF), the spectra of the photoluminescent response collected from the output end of the NV-center-doped PCF

(curve 1 in Fig. 2(a)) are almost identical to the spectra measured from an ensemble of nanoparticles in a cell or on a substrate

(curve 3 in Fig. 2(b)). These spectra display well-resolved peaks centered at 575 and 637 nm, corresponding to the ZPLs of the

neutral (NV0) and negatively charged (NV-) NV centers in diamond. At low densities of NV centers in the PCF, however, the

photoluminescence spectra collected from the PCF become distorted by the Raman signal (curve 1 in Fig. 2(b)), which is

inevitably generated by the optical pump in silica inside the fiber (curve 2 in Figs. 2(a) and 2(b)). In the PCF format, the level

of the Raman background can be radically reduced by increasing the air-filling fraction in the PCF. For a PCF shown Fig. 1(a),

the high air-filling fraction of the cladding allows the 637-nm ZPL line of NV-centers to be reliably detected against the

Raman background (curve 1 in Fig. 2(b)) for the density of NV centers in the fiber as low as 103

per 1 cm of fiber.

Figure 2. Spectra of NV center emission from a nanodiamond-doped ultrasmall-core PCF (1), the Raman background from the same fiber (2), and NV

center emission from a glass substrate (3). The density of NV centers is 5·104

(a) and 103

(b) per 1 cm of fiber.� (c) Spectra of NV center emission from a

nanodiamond-doped hollow-core PCF (1), 532-nm excitation radiation (2), and fiber transmission (3).

The ZPL-signal-to-Raman-background ratio for NV-center-doped fibers can be further improved with a hollow-core PCF

fiber design. For efficient excitation of NV centers and enhanced coupling of the ZPL photoluminescent response of these

centers to the fiber modes, hollow PCFs should be designed in such a way as to support the air guiding for both pump and ZPL

photoluminescence of NV centers with a maximum possible overlap of the radial profile of the pump field with diamond

nanoparticles deposited on the walls of the hollow fiber core (Fig. 1(b)). These somewhat conflicting requirements are fulfilled

with a hollow PCF structure used in our experiments. This fiber supports air-guided modes of the pump field, whose carrier

frequency is, however, off the center of the transmission band of the PCF (cf. curves 2 and 3 in Fig. 2(c)), providing for the

spatial overlap between the pump field and the diamond nanoparticles. The photoluminescence spectrum of the NV centers is,

on the other hand, matched with the transmission spectrum of the fiber (cf. curves 1 and 3 in Fig. 2(c)), providing efficient

coupling of the photoluminescence response from the NV centers to the air-guided modes of the PCF, thus allowing fiber-

format filtering of this signal from the Raman signal generated in the fiber cladding. This fiber design provides high ZPL-

signal-to-Raman-background ratios even at low levels of nanodiamond doping. For a density of NV centers of 104

per 1 cm of

PCF, the contribution of the Raman background to the overall output signal is below 1%, allowing a reliable detection of the

ZPL response from NV centers.

[1]J. Wrachtrup, S. Ya. Kilin, and A. P. Nizovtsev, Opt. Spectrosc. 91, 429(2001).

[2]T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J.R. Rabeau, N. Stravrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P.

R. Hemmer, and J. Wrachtrup, Nat. Phys. 2, 408 (2006).

[3]I. Aharonovich, A. D. Greentree, and S. Prawer, Nat. Photonics 5, 397(2011).

[4]L. P. McGuinness, Y. Yan, A. Stacey, D. A. Simpson, L. T. Hall, D.Maclaurin, S. Prawer, P. Mulvaney, J. Wrachtrup, F. Caruso, R. E. Scholten, and

L. C. L. Hollenberg, Nat. Nanotechnol. 6, 358 (2011).

[5]J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, Nat. Phys. 4, 810 (2008).

[6] G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, T. Hanke, A.

Leitenstorfer, R. Bratschitsch, F. Jelezko, and J. Wrachtrup, Nature 455, 648 (2008).

[7]T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Lonc ˇar, Nat. Nanotechnol. 5, 195 (2010).

[8] T. Schro ¨der, A. W. Schell, G. Kewes, T. Aichele, and O. Benson, Nano Lett. 11, 198 (2011).

[9] K.-M. C. Fu, C. Santori, P. E. Barclay, I. Aharonovich, S. Prawer, N. Meyer, A. M. Holm, and R. G. Beausoleil, Appl. Phys. Lett. 93, 234107 (2008).

[10] I. V. Fedotov, N. A. Safronov, Yu. A. Shandarov, A. Yu. Tashchilina, A. B. Fedotov, A. P. Nizovtsev, D. I. Pustakhod, V. N. Chizevski, T. V.

Matveeva, K. Sakoda, S. Ya. Kilin, and A. M. Zheltikov, Laser Phys. Lett. 9, 151 (2012).

[11] A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M.

Zheltikov, Laser Phys. Lett. 7, 46 (2010).

Simulation of Hyherfine Interactions

in a Large Carbon Cluster Hosting NV Center

A.P. Nizovtsev1, S.Ya. Kilin

1, A.L. Pushkarchuk

2, V.A. Pushkarchuk

3, F. Jelezko

4

1B.I. Stepanov Institute of Physics NASB, Nezavisimosti Ave. 68, 220072 Minsk, Belarus apniz@ifanbel. bas-net.by

2Institute of Physical Organic Chemistry NASB, Surganova 13, 220072 Minsk, Belarus 3BSUIR, ul. P. Browka 6, 220013 Minsk, Belarus

4Institute for quantum optics, Ulm University, Albert-Einstein Allee 11, 89069 Germany

Abstract: We have simulated hyperfine interactions in the C291NVH172 cluster for all possible po-

sitions of the 13C atom and demonstrated good correspondence of calculated ODMR spectra with

experimental data by Dreau et al. Phys. Rev. B 85, 134107 (2012).

1. Introduction

The ability to create, control and measure the coherence in multi-spin systems in solids is crucial for scalable

applications of quantum information processing, quantum sensing and metrology. Coupled electron-nuclear spin

systems where electrons act as fast processing qubits while nuclei can store quantum information for a long time

owing to their exceptional isolation from environment are especially useful for the purposes.

The most successful and promising representative of such systems is the nitrogen-vacancy (NV) color cen-

ter in diamond [1] whose ground-state electron spin (e-spin) S=1 is coupled to the nuclear spin (n-spin) I(N)=1 of

its own 14N atom and, potentially, to nearby n-spins I(C)=1/2 of isotopic 13C atoms that are distributed randomly

in diamond lattice with the 1.1% probability. Hyperfine interactions (hfi) in such systems lead directly to a few-

qubit gates which can be implemented using a sequence of optical, microwave or radio frequency pulses to ini-

tialize, coherently manipulate and readout the electron-nuclear spin system states [2-4]. Initially, it has been

done [3] on single NV centers strongly coupled to a 13C n-spin being nearest neighbor of the vacancy. Later [2,4]

more distant 13C nuclear spins located in the third coordination sphere have been distinguished in optically de-

tected magnetic resonance (ODMR) spectra and spin echo modulation. Most recently usage of dynamical de-

coupling methods to suppress background spin noise allows to observe single NV centers coupled to much more

distant single 13C nuclear spins and to study them systematically [5-9]. Here, we report on the systematic study

of hyperfine interactions between the electronic spin of single NV center and 13C nuclear spins in the NV-

hosting H-terminated carbon cluster C291NVH172 using computational chemistry simulation.

2. Methods and results

The geometric structure of the cluster was optimized and the spin density distribution was calculated by DFT

using the B3LYP1 functional with the MINI/3-21G basis sets. The calculations have been performed for singly

negatively charged cluster in the triplet ground state (S=1). We used the PC GAMESS (US) and ORCA software

packages to calculate hfi matrices for all possible positions of the 13C atom in the cluster. To be general, it has

been done in the same coordinate system - namely, the principle axis system (PAS) of the NV center where the

Z axis coincides with the C3V symmetry axis of the center while the X and Y axes are chosen arbitrarily. For

each 13C lattice position one can converts the calculated hfi matrix into diagonal form by transformation from the

NV PAS to the 13C PAS with elements of transformation matrix being the direction cosines between various

axes of both PASs. Evidently, various 13C lattice sites showed different and generally anisotropic interactions

with the NV e-spin, leading to different spin properties of various NV+113C spin systems.

The simulated hfi matrices have been used in the standard spin Hamiltonian of an arbitrary 14NV+113C sys-

tem that took into account i) zero-field fine structure splitting of the 3A ground-state of the center in a diamond

crystal field, ii) hfi of the S=1 e-spin of the NV center with I=1 n-spin of the 14N atom of the center, iii) the

quadrupole moment Q=1 of the 14N nucleus, iv) hfi with the I=1/2 n-spin of a 13C nucleus disposed somewhere

in the cluster and v) Zeeman interactions of all three spins with arbitrarily directed external magnetic field. Nu-

merical diagonalization of these spin Hamiltonians provides 18 eigenenergies and respective 18 eigenstates of

all possible 14NV+113C spin systems in the cluster.

Using this approach we have simulated ODMR spectra of 14NV+113C spin systems and compare them with

those experimentally observed in [6]. A typical hfi structure of e.g. mS=0 mS=-1 line in the ODMR spectrum

of a three-spin 14NV+113C system in a low magnetic field consisted of six lines corresponding to allowed EPR

transitions in the system with their frequency differences determined by the hfi with the 14N and 13C nuclear

spins. From these ODMR spectra one can extracts zero-field splittings 0i of e.g. the mS=-1 NV e-spin state

2

resulted from the hfi with single 13C n-spin taking specific (i-th) position in the cluster. If we compare these ex-

perimental data with those obtained by spin Hamiltonian method using simulated hfi matrices for all possible 14NV+113C system we will be able to address the specific 13C nucleus among other positions.

Calculations showed that owing to the C3V symmetry of the NV center there are NC (=3 or 6) positions of 13C nuclei in the cluster exhibiting very close values of 0i . These sets of near-equivalent lattice sites can be

termed as “families” [6]. We are presenting in the report the data for 26 such families named by English alpha-

bet letters A-Z with indication of average splittings 0i , Z coordinates, distances from Z-axis and from N atom

of the NV center which all are characteristic for each family. Another characteristic feature of families is the

absolute value of the cosine between the Z axis of the NV PAS and the z axis of the respective 13C PAS. It fol-

lows from the calculated values of cos(Zz) that there are few families for which the principle z axes of 13C nu-

clear spins are aligned rather close to the NV symmetry Z axis. At the same time it should be noted that exact

coincidence of the n-spin quantization axis with that of the e-spin of the NV center takes place only for the 13C

atoms located on the NV symmetry axis. For the cluster there are three such positions. For the nearest-to-

vacancy on-NV-axis position we predict the zero-field hfi splitting of 187.4 kHz.

0 10 20 30 40 50 600

2

4

6

8

10

12

14

Number of carbon-13 position in the cluster

Zero

-fiel

d hf

i spl

ittin

g (M

Hz) A

B

C

D

FG,H I,J K,L M,N

E

Fig. 1. Calculated values of hfi splittings (left) vs. those measured in [6] (right).

Fig. 1 show comparison of calculated values of hfi splittings 0i with those experimentally measured in [6].

Both figures clearly exhibit discrete values of hfi splittings, corresponding to different families. Their near coin-

cidence demonstrates that hfi parameters simulated by DFT for the C291NVH172 cluster in conjunction with spin

Hamiltonian method provide rather good fit to experimental splittings, allowing simultaneously address possible

positions of 13C in diamond lattice as belonging to specific family. Moreover, we were able to describe well the

experimental ODMR spectra shown in [6] for the specific 14NV+113C spin system.

References

[1] F. Jelezko, J. Wrachtrup, ”Quantum information processing in diamond”, J. Phys. Condens. Matter 18, S807-S824 (2006).

[2] L. Childress, M.V. Gurudev Dutt, J.M. Taylor, A.S. Zibrov, F. Jelezko, J. Wrachtrup, P.R. Hemmer, M.D. Lukin, “Coherent dynamics

of coupled electron and nuclear spin qubits in diamond,” Science 314, 281-285 (2006).

[3] F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and

realization of a two-qubit conditional quantum gate” Phys. Rev. Lett. 93, 130501 (2004).

[4] P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup, “Multi-

partite entanglement among single spins in diamond”, Science 320, 1326-1329 (2008).

[5] B. Smeltzer, L. Childress, A. Gali, “13C hyperfine interactions in the nitrogen-vacancy centre in diamond,” New J. Phys. 13, 025021

(2011).

[6] A. Dreau, J.-R. Maze, M. Lesik, J.-F. Roch, and V. Jacques, “High-resolution spectroscopy of single NV defects coupled with nearby 13C

nuclear spins in diamond”, Phys. Rev. B 85, 134107 (2012).

[7] N. Zhao, J. Honert, B. Schmid, M. Klas, J. Isoya, M. Markham, D. Twitchen, F. Jelezko, R.-B. Liu, H. Fedder and J. Wrachtrup,

“Sensing single remote nuclear spins”, Nature Nanotechnology 7, 657-662 (2012).

[8] S. Kolkowitz, Q.P. Unterreithmeier, S.D. Bennett and M.D. Lukin, “Sensing distant nuclear spins with a single electron spins,” Phys. Rev. Lett. 109, 137601 (2012).

[9] T. H. Taminiau, J. J. T. Wagenaar, T. van der Sar, F. Jelezko, V.V. Dobrovitski, and R. Hanson, ”Detection and control of individual

nuclear spins using a weakly coupled electron spin”, Phys. Rev. Lett. 109, 137602 (2012).

Long and Intermediate-Distance Qudit-Type Optical

Entanglement by Means of Weak Local Cross-Kerr

Nonlinearity

Alexander B. Mikhalychev, Sergei Ya. Kilin B.I. Stepanov Institute of Physics, NAS of Belarus, Nezavisimosti ave., 68, Minsk, Belarus

[email protected]

Abstract: We provide a protocol for qudit-type entanglement generation between two

optical field modes, separated by lossy medium and distance up to 100 km, using weak local

cross-Kerr interactions and linear optical scheme for probabilistic entanglement enhancement.

1. Introduction

Entanglement represents an important feature of quantum objects, being not only interesting from the theoretical

point of view, but also crucial for different tasks of quantum information processing (quantum teleportation,

quantum voting, distributed quantum computation, quantum cryptography). Of special interest is entanglement

generation at the distances from tens to hundreds of kilometers between sites, separated by noisy medium.

Here we consider the task of generating entangled states of optical field modes, belonging to distant

observers, with a lossy quantum channel connecting them. The resource, used for entanglement generation is a

weak local cross-Kerr interaction, available at both sites.

2. Local cross-Kerr interaction as a resource for entanglement generation

Cross-Kerr interaction itself can be used for generating entangled states starting from uncorrelated states of a

pair of quantum objects. Suppose a field mode c in a coherent state | c interacts with another system (another

optical field mode a [1-8] or an atomic system [9-11]). Due to the interaction, the phase of the coherent state

amplitude of mode c is shifted by the value, proportional to the number of excitations n of the system a:

| | | | i na c a cn n e , where describes the effective strength of the interaction. If the initial state of the

object a is a superposition of states with different excitation number (e.g. a coherent state | a in the case of

field mode), the final state of the considered system will be an entangled state, composed by pairwise

combinations of coherent states with different phases of mode c and number states of the system a (Fig. 1(a)).

The situation gets more complicated when a dissipative medium between final carriers of the entangled state

is taken into account. The transmitted filed cannot have large amplitude (otherwise decoherence rapidly destroys

all the quantum correlations). Experimentally observed interactions are also characterized by small strength

parameters . The magnitude of phase space displacement caused by such cross-Kerr interaction is

proportional to 1, and in general the final state is weakly entangled (Fig. 1(b)). Therefore, this simple

scheme is not applicable for generating strongly entangled states when the sites are separated by noisy media,

and a more sophisticated scheme, including some kind of entanglement enhancement, is required.

(a) (b) (c)

Fig. 1. (a) Entanglement generation by nonlinear interaction. (b) Entanglement generation between sites, separated by noisy medium.

Only weak entanglement can be generated. (c) Entanglement generation between sites, separated by noisy medium, with probabilistic

entanglement enhancement. Strongly entangled states are available in the case of successful measurement outcome.

One way of obtaining strongly entangled quantum state is to implement entanglement distillation. This

approach requires storage of quite a large number of initial weakly entangled states and can be quite

challenging. Another solution of the problem can be based on probabilistic entanglement enhancement [1-6, 10].

For this purpose one can design certain measurement, carried out at Bob’s site, with successful outcome

transforming initial weakly entangled state into a strongly entangled state. Direct measurement of the state of

field mode c makes this mode inaccessible for any further use. Measurements, implemented with linear optics

and photodetectors not resolving photon number on field modes, obtained by splitting mode c, completely

determine the state of the mode and destroy entanglement. Therefore, some kind of nonlinearity is required at

Bob’s site, too. It is quite natural to suppose that this nonlinear interaction is the same as the one at Alice’s site

(see, e.g., Refs. [1-6, 10] and Fig. 1(c)).

3. Scheme of entanglement generation and enhancement

Several schemes, based on probabilistic entanglement enhancement by a measurement at Bob’s site, have

already been proposed for entangling distantly separated field modes, when effective strength of nonlinear

interactions is equal to (strong nonlinear interaction) [2], and for entangling atomic qubits [10], as well as

for creating qubit-type entangled states of optical field modes [3-4], when only small nonlinearity is available.

In our recent papers [1, 5, 6] a more general task was solved: the designed measurement scheme was

capable for creation of an arbitrary qudit-type state (including entangled states) from a wide class of possible

states in a continuous variable system using weak cross-Kerr nonlinearity, linear optical devices, detectors, and

sources of coherent states. The entanglement enhancement (more precisely, conversion of the weakly entangled

initial state into the desired final state) is carried out by discrimination of an appropriate state of the mode cfrom the set of its most probable states. For this purpose a concept of elimination measurements was introduced

and their realization for coherent states on the basis of linear optics was provided.

In Refs. [1, 5, 6] the case of long distances between Alice and Bob was considered, and the state of the

mode c belonged to the linear span of Fock states with few photons. For intermediate distances (about 10-

50 km) the used assumption of small amplitudes 1 becomes invalid. In this contribution we generalize the

entanglement enhancement scheme for arbitrary amplitudes , thus making the entanglement generation

protocol efficient for the both cases of long and intermediate distances.

Fig. 2 illustrates the protocol of entanglement generation. The measurement scheme is based on

discrimination of the state | c , defined from the equation 0 f| |c abc ab , where 0| abc is the initial 3-

modes weakly correlated state and f| ab is the desired final state. The discrimination procedure consists in

carrying out elimination measurements for a set of coherent states, determined in the unique way by cross-Kerr

nonlinearity, the desired final state and the attenuation in the quantum channel between the sites. We prove

realizability of the protocol in realistic conditions and show that it can be used for generating entanglement,

large than the limit for a pair of qubit systems.

Fig. 2. Scheme of entanglement generation. Alice prepares an entangled state of field modes a and c; then she sends ancillary mode cand reference mode d through the quantum channel to Bob. Having correlated the states of modes b and c, Bob measures the final state of

the ancillary field mode c (with the help of reference mode d) and, in the case of successful outcome, announces to Alice under the classical

channel that entanglement was generated (otherwise the set of operations is repeated).

[1] S. Ya. Kilin and A. B. Mikhalychev, “Optical qudit-type entanglement creation at long distances by means of small cross-Kerr

nonlinearities,” Phys. Rev. A 83, 052303 (2010).

[2] S. Ya. Kilin and A. B. Mikhalychev, “Continuous variable entanglement creation over long distances,” Proc. SPIE 6726, 67263D

(2007).

[3] S. Ya. Kilin and A. B. Mikhalychev, “Long distance entanglement of continuous variables in fiber,” Nonlinear Phenom. Complex

Syst. 12, 150 (2009).

[4] S. Ya. Kilin and A. B. Mikhalychev, “Creation of entanglement of continuous variables using small Kerr nonlinearity,” Opt.

Spectrosc. 108, 178 (2010).

[5] S. Ya. Kilin and A. B. Mikhalychev, “Qudit-type entanglement of continuous variables via weak cross-Kerr nonlinearity,” Opt.

Spectrosc. 111, 547 (2011).

[6] S. Ya. Kilin and A. B. Mikhalychev, “Weak cross-Kerr nonlinearity as a resource for quantum state engineering,” Nonlinear

Phenom. Complex Syst. 14, 1 (2011).

[7] T. Tyc and N. Korolkova, “Highly non-Gaussian states created via cross-Kerr nonlinearity,” New J. Phys. 10, 023041 (2008).

[8] D. Mogilevtsev, T. Tyc, and N. Korolkova, “Influence of modal loss on quantum state generation via cross-Kerr nonlinearity,”

Phys. Rev. A 79, 053832 (2009).

[9] P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using

bright coherent light,” Phys. Rev. Lett. 96, 240501 (2006).

[10] S. G. R. Louis, K. Nemoto,W. J. Munro, and T. P. Spiller, “Weak non-linearities and cluster states,” Phys. Rev. A 75, 042323

(2007).

[11] T. D. Ladd et al., “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent

light,” New J. Phys. 8, 184 (2006).

Statistical entropy of radiation and its increase due to finite beam aperture

A.V. Shepelev

I.M. Gubkin Russian State University, Moscow, Leninsky pr., 65

[email protected]

Abstract: The basic concepts of radiation entropy are analyzed, the most commonly used in

quantum optics and quantum information processing. Their peculiarities and disadvantages

are discussed. If excluding the interaction of radiation with an optical system, the von

Neumann’s entropy is not an invariant of the system and is close to the Planck’s entropy of

for the thermal radiation. For this situation, the entropy increase due to the finite aperture

and beam splitting is calculated.

Statistical (not thermodynamic) definition of entropy, that is required to adequately address many

of the problems of quantum optics and quantum information, is based either on maintaining the Lebesgue’s

measure in the Liouville’s theorem, or on a unitarity of the transformation. The result of this is the fact that

the entropy of a closed system is invariant. To date, a number of definitions of the entropy of the radiation

have been proposed (by Planck, von Neumann, Shannon, Werhl, and others). Comparison of these

definitions shows that the most consistent is the von Neumann’s entropy, which is expressed through the

density matrix. However, the entropy operator is not defined; for the entangled states the von Neumann’s

entropy can be equal to zero, whereas for each of the marginal states it differs from zero.

If excluding the variables, which concern the parameters of matter, conversion of the incident-field

characteristic function to the scattered-field one is not unitary, and can not be described by the

Schrödinger’s equation, but can be described by the kinetic equation. In this case, the von Neumann’s

entropy for the thermal radiation coincides with the Planck’s entropy (applicable to systems of non-

interacting bosons) after replacing term "brightness" to the term "photon / mode". In undertaking such a

conversion, it becomes possible to perform the calculation of increase of the radiation entropy under a

spatial diaphragming of light beams, as well as under splitting.

Beam splitting leads to an increase in the total entropy of the radiation, which is in full compliance

with the requirements of thermodynamics. Calculation of entropy for centrosymmetric beams shows an

increase of entropy due to the finite typical size of an aperture d . A monotonic variation of entropy takes

place when the parameter dλ grows up. Entropy depends on the profile of the beam, the lower entropy

then corresponds to a Gaussian profile. The general criterion is established for the beam profile or the

aperture of the radiating system, in which the entropy of thermal radiation is minimal.

Resonance fluorescence of one and two atoms in feedbackloop

L.V. Il’ichov a,b and V.A. Tomilin a,b,c

a Institute of Automation and Electrometry SB RAS, 630090 Novosibirsk, Russia,b Novosibirsk State University, 630090 Novosibirsk, Russia,c Ecole Politechnique, 91127 Palaiseau Cedex, France.

E-mail: [email protected] and [email protected]

Abstract. We study the resonance fluorescence spectrum and photoemission statistics oftwo-level atom in classical light field with sign switching upon every detection of spontaneousphoton. The statistics in the case of two atoms is also considered.

Open quantum systems exchanging energy and information with the environment caneffectively control their own evolution. The scheme with a photon source connected to thedetector via feedback loop is the most interesting and useful for applications [1].

Within a simple model system [2], we evaluated the spectrum of resonance fluorescenceof a two-level atom under the presence of feedback. The pumping monochromatic light fieldwas considered classical, with phase switching by π every time the spontaneous photon isdetected. A small part of fluorescence was assumed to undergo spectral measurement. It wasdiscovered that spectrum has some similarities with a well-known Rautian-Mollow tripletstructure. But the sidebands’ amplitudes appear to get drastic asymmetry under non-zerofield frequency detuning from the atomic transition. Moreover, the spectrum preserves aclearly visible triplet structure even beyond the secular approximation, when the sidebandsin Rautian-Mollow structure become indistinguishable.

It is also of interest to study how the feedback affects the resonance fluorescenceproperties like emission statistics, that are complementary in quantum sense to the spectralones. It is not hard to see that introduction of the feedback phase switching cannot changesthe satistics in the limit, when photoemissions are treated as precisely time-localized events.Really, after the registration of such a photoemission, the atom finds itself in the groundstate. There is neither coherence between excited and ground states, no memory aboutprevious field phase. Due to this reason phase switching will not affect the probability ofnext photoemission. For two or more atoms the situation is completely different. Now thephotodetection does not bring the system to the ground state for sure. One atom is still ableto preserve the coherence and the memory about the phase of light before the photodetectionevent. In [3] the photoemission statistics of a pair of atoms was studied, and it was found thatsignificant antibunching that takes place even without the feedback phase switching, can bedramatically increased when introducing the last one.

2

Coming back to the case of one atom, one can see that the founded resistant triplet struc-ture of the spectrum of resonance fluorescence naturally poses the question about the photoe-mission statistics in triplet components taking separately and about the correlations betweenthem. Such formulation of the problem means ’soft‘ spectral selection of emitted photons.This selection takes small, but finite time, and so the instant of photodetection cannot belonger identified with that one of photoemission. In between these two instants atom con-tinues evolving in the light field with the previous phase, acquires the coherence betweenlevels and so preserves the memory about the phase after its switching. It was found that thedistribution of photocounts in the central peak remains Poissonian, as it was in the absenceof the feedback. However, a statistical dependence appears between the photoemissions firstto the central peak and then to a side one. There take place correlations as well as anticor-relations depending on the value of detuning. In the resonance fluorescence of a two-levelatom without feedback the antibunching in every sideband is observed [4]. Due to feedback,the photocounts in every sideband component acquire super-Poissonian statistics. Photoemis-sions first to one and then to another sideband are anticorrelated, i.e. the situation appears tobe in some sense ’inverted‘ with respect to case with no feedback.

[1] Wiseman H and Milburn G 2010 Quantum Measurement and Control (Cambridge University Press)[2] Tomilin V A and Il’ichov L V 2011 JETP Letters 94, 9[3] Tomilin V A and Il’ichov L V 2013 JETP 116, No 2[4] Carmichel H J and Walls D F 1976 J. Phys. B 9 1199

Generation of arbitrary symmetric entangled states

with conditional linear optical coupling A. V. Sharypov

Kirensky Institute of Physics, 50 Akademgorodok, Krasnoyarsk, 660036, Russia and

Siberian Federal University, 79 Svobodny Ave., Krasnoyarsk, 660041, Russia

[email protected]

Bing He

Institute for Quantum Information Science, University of Calgary, Calgary, Alberta T2N 1N4, Canada

[email protected]

Abstract: An approach for generating the entangled photonic states

1221 ΨΨ±ΨΨ from two arbitrary states 1Ψ and 2Ψ is proposed. The

protocol is implemented by the conditionally induced beamsplitter coupling which

leads to the selective swapping between two photonic modes.

�

1. Introduction

Bipartite symmetric entangled states refer to a generic type in the form 1221 ΨΨ±ΨΨ up to a

normalization factor. Such entangled states include the symmetric entangled coherent states (SECSs)

αββα ± [1] and the N00N states NN 00 ± [2, 3]. Both of them have found important

applications in quantum metrology; see, e.g. [4, 5]. A SECS of light fields can be transformed to a

photonic Schrodinger cat state γγ −± [6] simply by a beam-splitter (BS) operation.

In this poster we provide a method for generating arbitrary symmetric entangled photonic states

1221 ΨΨ±ΨΨ from two arbitrary states 1Ψ and 2Ψ � ��The protocol is implemented by

the conditionally induced beamsplitter coupling which leads to the selective swapping between two

photonic modes. Such coupling occurs in a quantum system prepared in the superposition of two

ground states with only one of them being involved in the swapping.

2. The protocol

To entangle the two photonic states 1Ψ and 2Ψ , we also need an ancilla quantum system with

two stable states m and g . This system can be an atom, as well as an ion, a quantum dot or a

superconducting qubit. The ancilla system is initially in state m , setting the initial state for the total

system as m210 ΨΨ=Φ . Then we perform a xσ �rotation between m and g and transfer

the system to the superposition

( ) 2/211 gim −ΨΨ=Φ (1)

The above superposition of m and g works as a logic control on the swapping between two input

photonic modes: the swapping between the photon modes is activated in the | g subspace and

does not happen in the m subspace. Such conditional swapping can be realized by BS

transformation via the dispersive parametric three-wave mixing (TWM) [8, 9] or four-wave mixing

(FWM) [10, 11] process. The conditional swapping results in the state

( ) 2/12212 gim ΨΨ−ΨΨ=Φ (2)

Then, again we perform a xσ � rotation between m and g to have them transformed as

( ) ( ) ( )mgigmgm −→ , leading to the following state

( ) ( )[ ]gim 122112213 2

1 ΨΨ+ΨΨ−ΨΨ−ΨΨ=Φ (3)

Finally, by measuring m and g , we make the photonic sector of the total state collapse to the

target symmetric entangled states 1221 ΨΨ±ΨΨ . A candidate for the ancilla system should

satisfy two requirements. First, the quantum system should have two long-lived and well separated

states between which a xσ rotation can be performed. The second requirement is specified by the

swapping stage—the system should have an appropriate energy level structure for the formation of

the TWM or FWM interaction loop where two of the transitions have to be strongly coupled to the

input fields. These conditions can be satisfied by certain trapped natural atoms or ions, single color

centers, quantum dots or superconducting qubits based on the Josephson junctions, which have

multi-level structures and can also be strongly coupled to the suitable field modes.

3. References

[1] B. C. Sanders, J. Phys. A: Math. Theor. 45, 244002 (2012).

[2] B. C. Sanders, Phys. Rev. A 40, 2417 (1989).

[3] A. N. Boto, et al., Phys. Rev. Lett. 85, 2733 (2000).

[4] H. Lee, P. Kok, and J. P. Dowling, J. Mod. Opt. 49, 2325 (2002).

[5] T. C. Ralph, Phys. Rev. A 65, 042313 (2002).

[6] S. Glancy and H. M. Vasconcelos, J. Opt. B: Quantum Semiclassical Opt. 25, 712 (2008).

[7] A.V. Sharypov and B. He, arXiv:1211.3330 (2012).

[8] R. M. Serra, et al., Phys. Rev. A 71, 045802 (2005).

[9] G.-W. Lin, et al., Phys. Rev. A 77, 064301 (2008).

[10] D. D. Yavuz, Phys. Rev. A 71, 053816 (2005).

[11] A. V. Sharypov, X. Deng, and L. Tian, Phys. Rev. B 86, 014516 (2012).

Emergence of time from static entangled states

M. Genovese1, M Gramegna1, L. Maccone2, E.V. Moreva1,3

1INRIM, I-10135, Torino, Italy 2Universita' di Pavia, I-27100, Pavia, Italy

3Moscow National Research Nuclear University MEPHI , 115409, Moscow, Russia

Abstract We experimentally demonstrate the proposal by Page and Wootters that time may emerge

from a static (with respect to an abstract external time) entangled state. Even though the total

state of a system is static, time is recovered as correlations between a subsystem that acts as

a clock and the rest of the system that evolves according to such clock. We use a system

composed of two entangled photons: the rotation of the polarization of the first acts as a clock

for proving an evolution of the polarization of the second. Nonetheless, we prove that the

joint polarization state of both photons does not evolve.

Essentially, the problem of time [1, 2] in physics consists in the fact that a straightforward

quantization of the general relativistic evolution equation and constraints generates the

Wheeler-De Witt equation 0totH , where totH is the global Hamiltonian of the universe

and 0 is its state. Obviously, this means that the state of the universe must be static,

which clashes with our everyday experience of an evolving world.

Apart from the Wheeler-De Witt equation, one can also imagine that a time shift of

the state of the whole universe must be unobservable from a purely physical consideration: if

you shift the state of the whole universe, there is nothing external that can keep track this

shift, so this shift must be unobservable.

Page and Wootters idea[3, 4] is based on the fact that there exist states of a system

composed by entangled subsystems that are stationary, but one can interpret the component

subsystems as evolving. One can then suppose that the global state of the universe as one of

this static entangled state, whereas the state of the subsystems (us, for example) can evolve.

This solves in an extremely elegant way the problem of time.

The idea for the experiment is extremely simple: we just want to show that a static

entangled state can have subsystems that evolve. We also want to show that the

property of being static is unaffected by the measurement.

The experimental apparatus is depicted in Fig. 1. It consists in two different settings. In Fig.

1(a) the apparatus is in observer mode, where we are the observers. In Fig. 1(b) the

apparatus is in super-observer mode, where we are considering the universe from the

outside and we perform a measurement on the whole system.

Experimental apparatus. (a) Experiment to prove that one subsystem (polarization of the upper photon) evolves

with respect to a clock constituted by the other subsystem (polarization of the lower photon). (b) Experiment to

prove that the global state of the system is static, even after the measurement is performed. The beam splitter

(BS) is performing a quantum erasure of the polarization measurement performed by the polarizing beam

splitter PBS. The squares represent polarizing beam splitters in the , basis, the blue boxes represent

different thicknesses of a birefringent material which provide evolution of a state. Different thicknesses

represent different time evolutions. The dashed box represents the (known) phase delay of the clock photon

only.

In the first experiment , which corresponds to observer mode (Fig.1(a)), where we have

shown that one photon evolves if we use the other photon as a clock.

In the super-observer mode ((Fig.1(b))), the global state of the two photons is static with

respect to any external clock. We have proven it by way of measuring of fidelity between

input state and output one for different values of an external time (different slabs of a

birefringent material).

[1] E. Anderson, The Problem of Time in Quantum Gravity , arXiv:1009.2157v2 (2010).

[2] R.D. Sorkin, Int. J. Theor. Phys. 33, 523 (1994).

[3] D.N. Page and W.K. Wootters, Evolution without evolution: Dynamics described by

stationary observables , Phys. Rev. D 27, 2885 (1983).

[4] W.K. Wootters, Time Replaced by Quantum Correlations , Int. J. Theor. Phys. 23, 701

(1984).

Self-induced polariton resonant nanocavities

V.S. Egorov 1, V.G. Nikolaev

2, I.A. Chekhonin

1, M.A. Chekhonin

2, S.N. Bagaev

3

1St.Petersburg State University, Department of Optics, Ulianovskaya 1, Petrodvorets, 198504, St.Petersburg, Russia. 2St.Petersburg National Research University of Information Technologies, Mechanics and Optics, Kronverkskiy pr. 49, 197101

St.Petersburg, Russia 3Institute of Laser Physics, Siberian Branch of the Russian Academy of Sciences, Lavrentyeva 13/3, 630090 Novosibirsk, Russia

E-mail: [email protected]

The properties of coupled long-lived states of “field + matter” system produced by collision of

two counter-propagating coherent pulses in the dense resonant media are discussed. It was

shown that system reveals properties of polariton nanocavity with high Q-factor.

The coupled long-lived states of the system “field + matter” can be produced in a single-mode microcavities

[1]. Using the ansatz (1) of the rotation angle of a Bloch-vector (x,t), Maxwell-Bloch equations can be reduced

to nonlinear pendulum-type equation (2).

Kxttx sin, (1)

022

11

2

2

2

Jdtd

dtd

cc

(2)

cK 0 - wave vector of a resonant mode, c - decay time of a cavity, c - cooperative frequency [1],

J1( ) - Bessel function of the first kind of order one. Values of rotation angle m= ±7.02, ±13.32 … (J1( m) = 0)

corresponds to the coupled metastable states. The ground state of the system corresponds to m= 0.

The large lifetime of metastable states is the result of the absence of phase matching between the field E(t,x)

and polarization of the media P(t,x). When = m the spatial spectrum of resonant polarization contains only

wave vectors q = ± 3K, ± 5K, … and there is no radiation in the far field zone. The additional solutions of mode

instability problem and nonlinear superradiance phenomena in multimode cavity was derived in [2].

Present paper deals with processes of formation of coupled long-lived states of the system “field + matter”

during collision of two counter-propagating coherent pulses in resonant media.

The problem was studied by means of numeric solution of Maxwell-Bloch equation, without application of

slow envelope functions approximation (RWA) of the field E(t,x), polarization P(t,x) and population differences

N(t,x). We took into account finite relaxation times 1 and 2 during the consideration.

It was shown, there exists a threshold value of pulse area (t = ) 0.55 which results into self-induced

polariton resonant nanocavities to appear. At the Fig. 1 the spatial-temporal evolution of population difference

N(t,x) after collision of two - pulses is presented. The point of collision corresponds to Kx = 300.

After collision of two 2 -pulses (Fig. 2) strongly localized stationary coupled state of the field and matter is

produced. If one refuses from slow envelope functions formalism respectively to x-axis, the mode of

nonperturbing propagation of 2 -solitons, being developed in self-induced transparency theory (SIT), is no more

valid.

Spatial spectra of P(t,x) and N(t,x) in the range of coupled state were studied. The presence of a large

number of polarization P(t,x) spatial Fourier - components as well as the same of population difference was

shown. Wave numbers q of polarization appeared to be ± 3K, ± 5K, ± 7K … , and those of population

difference 2K, 4K, 6K ...

Dynamics of radiation field of self-induced polariton resonant nanocavities in the near field and far field

zones of radiation was studied. It was shown that radiation in the far field zone is a superposition of upper and

lower exciton-polariton branchs of the system.

Group velocity of the far field zone radiation is negative and directed to the collision point of pulses. The

value of dispersion of the group velocity gives a width of a stop-band of a Bragg structure of self-induced

resonant nanocavities.

The probe pulse reflection process in a stop-band caused by collision of solitons of self-induced

transparency was studied as well [3].

Fig. 1. Spatial-temporal dynamics of N(t,x) of a coupled state under collision of two - pulses.

Density of atoms No = 6.0*1017 cm-3.

Fig. 2. Spatial-temporal dynamics of N(t,x) of a coupled state under collision of two 2 - pulses.

Density of atoms No = 1.5*1020 cm-3.

[1].V.S. Egorov, I.A. Chekhonin,"Metastable states in the system "field-matter" under the conditions of cooperative self-diffraction in a

resonator", Zh. Tech. Phys. 56, 572-574 (1986). [Sov. Phys.-Tech. Phys. 31, 344 (1986)].

[2]. V.V. Kocharovsky, Vl.V. Kocharovsky, E.R. Golubyatnikova “Mode instability and nonlinear superradiance phenomena in open Fabry-

Perot cavity”, Computers & Mathematics with Applications, 34, 773-793 (1997).

[3]. D.V. Novitsky, “Controlled absorption and all-optical diode action due to collisions of self-induced-transparency solitons”, Phys. Rev.

A 85, 043813-1-7 (2012).

Theory of Open Quantum Systems

Based on Stochastic Differential Equations

A.M.Basharov National Research Centre “Kurchatov Institute”,

Kurchatov pl.1, Moscow 123182, Russia; e-mail address: [email protected]

Abstract: The evolution operator and the kinetic equation for the density matrix of an

open system are obtained to analyze the dynamics of localized open systems in the

Markov approximation.

It is shown that the effective Hamiltonian representation, as it is formulated in author’s papers [1-4],

serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent

noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the

Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open

system and its environment. General quantum stochastic differential equations of non-Wiener type for the

evolution operator and the kinetic equation for the density matrix of an open system are obtained, which

allow one to analyze the dynamics of a wide class of localized open systems in the Markov

approximation. The main distinctive features of the dynamics of open quantum systems described in this

way are the stabilization of excited states with respect to collective processes and an additional frequency

shift of the spectrum of the open system. As an illustration of the general approach developed, the photon

dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical

intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the

photons of the cavity mode are “locked” inside the cavity, thus exhibiting a new phenomenon of radiation

trapping and non-Wiener dynamics [4].

The main effect underlying described phenomena has been focused on the case that the low intensity

of the Stark interaction with a vacuum field, which is characteristic of an ordinary atom, becomes high

enough for an N-atom ensemble, as the Stark interaction ensemble operator is proportional to the number

of atoms N. Therefore, the Stark interaction with a vacuum field is enhancing in the ensemble of identical

atoms and can prove to be significant in the process of the collective decay and other processes if the

atoms number is high enough. As a consequence, the collective spontaneous emission (superradiance) can

be fully suppressed and the ensemble of excited atoms stops emitting if the atoms number coincides with

the critical atom number established in the paper. On the one hand, the result obtained offers a different

treatment of the optimum conditions for superradiance observation, while, on the other hand, it presents a

new fundamental effect – the stabilization of an ensemble of excited atoms against the collective

spontaneous decay. To some extent, this very stabilization effect is in an apparent contradiction with

superradiance [1,2].

[1] A.M.Basharov, The Stark interaction of identical particles with vacuum electromagnetic field as quantum Poisson process

suppressing collective spontaneous emission, Phys. Rev. A 84, 013801 (2011).

[2] A.M.Basharov, Inhibition of collective spontaneous decay and superradiance in an ensemble of sufficiently high quantity of

excited identical atoms, Physics Letters A 375, 2249–2253 (2011).

[3] A.M.Basharov, Quantum Theory of Open Systems Based on Stochastic Differential Equations of Generalized Langevin (non-

Wiener) Type, JETP 115, 371–391 (2012).

[4] A.M.Basharov, Radiation trapping in a high-Q cavity containing nonresonant atoms coupled with an external broadband vacuum

field, Physics Letters A 376, 1881-1888 (2012).

Entanglement dynamics of coupled oscillators under continuous

quantum measurements O.M. Kiriukhin*

Faculty of Physics, M.V. Lomonosov Moscow State University, Russia, Moscow, 119991, GSP-1, Leninskie Gory, 1, bld. 2 *[email protected]

Abstract: Future advanced gravitational-wave detectors and other optomechanical devices

will reach such high sensitivity that they possibly allow us to study quantum behaviors of the

macroscopic quantum objects [1]. One interesting issue, which is also of fundamental

importance, is the observation of the Einstein-Podolsky-Rosen-type of quantum entanglement

among macroscopic objects [2], for example, the kilogram scale test masses. We explore

dynamics of quantum entanglement and study the possibility of observing it with future

advanced gravitational-wave detectors or prototypes and other optomechanical systems. For

such systems we calculate logarithmic negativity [3] as a function of time. We show that

quantum entanglement is a result of dynamics of the system and at certain parameters it can

persist for an infinitely long time.

1. Introduction

Many scientific groups all over the world are trying to prove the universality of quantum mechanics and confirm

experimentally the applicability of quantum mechanics to macroscopic mechanical objects. If the success is

reached, it will have not only be of fundamental significance for understanding physical picture of the nature

that certainly in itself is a priority of modern physics, but also will open the new technological horizons for

development of quantum computer, quantum communications, quantum cryptography and quantum

calculations.

The optomechanical systems, in which light interacts with a reflecting mechanical object by means of

radiation pressure, became an ideal platform for studying macroscopic objects in quantum state.

The most significant implementation problems in these experiments arise from the fact that quantum states

are very sensitive to external influence and as a result of interaction with environment decay into classical

superposition. Therefore these experiments require systems to be isolated from external influences so that the

level of the classical noise which leads to decoherence wouldn't change the observable more than it's uncertainty

during the measurement process.

One of the most interesting experimental tasks in this area of fundamental physics is the direct

demonstration of the Einstein-Podolsky-Rosen paradox in its initial version [4], that is for coordinate and

momentum of mechanical objects. It would be an argument for applicability of quantum mechanics to

macroscopic mechanical objects. The explanation of Einstein-Podolsky-Rosen paradox leads to the conception

of quantum entanglement. It has been studied for many different systems, but for optomechanical systems only

stationary case has been considered. We are aiming to describe the dynamics of quantum entanglement of

mechanical degrees of freedom under continuous quantum measurements.

2. Model

We consider Michelson interferometer with two Fabry-P rot cavities in the arms in the scheme known as local

readout [5]. The system is driven by two pumps at different frequencies. We use the bad cavity approximation. It

takes place when the cavity effective optical bandwidth is larger than the mechanical frequency. In this case it is

possible to ignore the dynamics of the cavity-mode. Detuning of Fabry-P rot cavities creates an optical spring

[6] between input and end mirrors. It is supposed that continuous measurements of quadratures are being

performed in the dark port. One pump is responsible for the information about differential mode of input

mirrors, the other is responsible for the information about differential mode of end mirrors. Mechanical modes

are considered as oscillators coupled via optical spring. The system is linear and all the noises are Gaussian and

Markovian so the quantum state of it is fully described by the covariation matrix. We include dissipation

mechanism in the quantum Langevin equations which describe our system.

3. Conditional quantum entanglement

Measurements of a quantum system result in the reduction of its quantum state. We have to differ quantum state

of a system with measurements and quantum state of a system without measurements. Conditional quantum

state is defined as projection to the sub-space in which the readout observable has definite values. In most

general case in order to obtain conditional density matrix one must solve Stochastic Master Equation. But for

Gaussian systems it can be shown that it is equivalent to the direct application of Kalman-Belavkin filter [7]. It

minimizes dispersion and allows to recover maximum information of the conditional state from our

measurement.

4. Experimental proposal

For the parameters of our system we use characteristic parameters of Advanced LIGO [1]. We analyse the

dependence of logarithmic negativity on the different parameters of the system. From the Figure 1 we can see

that quantum entanglement oscillates with time. The entanglement decreases with the increase of the force noise

frequency F

, decrease of the sensing noise frequency X

and decrease of quantum efficiency . Squeezing

can enlarge entanglement in the system.

Figure 1. Plot of logarithmic negativity as a function of time St at different values of force noise frequency

F, mechanical q-factor

8

m 10Q , quantum noise frequency q / 2 100 Hz, sensing noise frequency X q3 , quantum efficiency 0.9 , homodyne

angle / 4 , squeezing factor 0q .

5. Conclusion

We have found that quantum entanglement oscillates with time and asymptotically reaches stationary value. The

main criteria for entanglement would be F q X , that is the classical noise must be below SQL. Thus,

SQL is a benchmark for MQM experiments with optomechanical systems.

6. References

[1] www.advancedligo.mit.edu.

[2] O. M. Kiriukhin, S. L . Danilishin, Dynamics of quantum entanglement in optomechanical systems with dissipation Moscow University Physics Bulletin, vol. 1, p. 120110, (2012).

[3] G. Vidal, R. F. Werner Computable measure of entanglement , vol. 65, p. 032314, (2002).

[4] A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev. 1935, vol. 47, pp. 777 780.

[5] H. Rehbein et al., Local readout enhancement for detuned signal-recycling interferometers Phys. Rev. D, vol. 76, p. 062002, (2007).

[6] S. L. Danilishin, F. Ya. Khalili, Quantum Measurement Theory in Gravitational-Wave Detectors Living Rev. Relativity, vol. 15, no. 5, (2012).

[7] V. P. Belavkin, Quantum continual measurements and a posteriori collapse on CCR Comm. Math. Phys, vol. 146, pp. 611 635,

(1992).

Manipulation of resonance fluorescence of the atoms or ions, which are subjected to

mechanical oscillations in a standing wave

Nicolae Enaki, Sergiu Bazgan

Institute of Applied Physics, Academy of Science of Moldova, Chisinau, Moldova

AbstractThis report is devoted to the problem of the resonance fluorescence of an atomic (or ion) system in the resonance

with driving the standing wave of the optical cavity. It is shown that in this case resonance fluorescence depends on

the location of atoms (or ions) relative to the positions of the nodes and antinodes of standing waves. It is

demonstrated that if the atoms perform mechanical oscillations relative to the equilibrium position like in Paul traps,

the distance between the Mollow type resonance fluorescence triplet is changed as a function of the frequency of

these oscillations. This effect is possible for two and three level system placed in two transversal standing waves of

the resonator. The dependence of the photon statistics on the applied mechanical oscillation is studied.

Summary

We consider the interaction of three level ion in interaction with two standing waves in the

resonance with the transitions of this ion. As two level system, can be obtained from the three

level system than one dipole active transition is considered equal to zero, we focus on the

description of three levels of Lambda type system in resonance with the two transversal dressed

standing waves of the resonator. Considering that the three level atoms interacts with two modes

of the standing waves 0 cos sin ,E E t k r , 1, 2 in resonance with the transitions

3d , we can represent the dressed Hamiltonian of this system by the expression

0 3

1.2 1

2

3 0

1 1

ˆ ˆ( )

ˆ ˆ exp[ ( , )(1 )] . . ,

N

j jj

N

j j j jj

H a a

a a i k r H c(1)

where the Rabi frequencies depend on the position of " " atom in the transversal standing

wave

0 0

0 3 0

sin( , ) 1

( , ) / 0

jj

forfor

k r

d E (2)

ˆ ja and ˆ ja are the creation and annihilation atomic operators on the state of three level

system, 3

represent the difference of energy between the level 3 and , is the

energy of the electromagnetic field, takes 1 and 0 values which correspond to the the

standing and travelling waves respectively. The cooperative spontaneous emission of the dressed

Lambda type three level radiator in the single mod traveling wave was studied in the paper

[Enaki & Svera, 1988] As was demonstrated recently the cooperative behavior of spontaneous

emission in standing wave have new peculiarities which depend on the atomic positions in the

standing wave [Enaki et all, 2011]. The resonance fluorescence of three level atom in the two

standing transversal wave opens the attractive applications due to the fact that the stopped atom

(or ion) can oscillates around the equilibrium position changing its interaction with the dressed

field. Considering that the radiator suffers the mechanical oscillation around the equilibrium

position in the antinode 0 cosj j mr r t with frequency m ( m j j ), we can obtain

the dressed states in the Hamiltonian (1) using the Bogoliubov transformation

1 1 2

1 01 1 3 22 2

2 2

1 1 2

2 02 1 3 22 2

2 2

3 1 3

1 1exp[ ( , )(1 )]

2 2

1 1exp[ ( , )(1 )]

2 2

1 /( )

2

j j jj j j j j

jj j j j

j j jj j j j j

jj j j j

jj j j

a i k r A A A

a i k r A A A

a A A

Here 3| | , 2 2

1 2j j j . After this transformation it is obtained three

new dressed Hamiltonian with the quasi-levels "i" with energies ji

0 1 1 1 2 2 2 3 3 3

1

,N

j j j j j j j j jj

H A A A A A A (3)

which depends on the vibration time 2 2 2

1(3) 1 2 22 4( ) ( ),j j j jt t through

mechanical oscillations of the nuclei in the standing wave 0 0 0sin[( , ) cos ]j mtk r . As

follows from the expression (3) the quasi-levels energy depends on the position of the radiators

relative the nodes and antinodes of the standing waves. So energy will depend on the frequency

and amplitude of oscillations of atoms relative to the position of equilibrium 0 cosj j mr r tand the position of this mechanical oscillator in the standing wave. Now we can introduce the

interaction of these dressed atomic systems with vacuum of electromagnetic field (EMF)2

3 3 1 1 3

3 1 3 1

1 1

1 1 3

(3 ) 2 2

( , ){[ ( )

2

2 ( 1) ( )] exp[ ( , )] . .}.

Nk

I j j j j jk j j

j j j k j

H U U U U

U U b i H c

g d

k r

Here we have introduced the new operators of the transitions between the dressed states abj ja jbU A A . For simplicity, the interaction Hamiltonian is obtained for deviation of resonance

0 . Using the method of elimination of the Bose operators [1,2], we have obtained the

Mollow triplets of the two dimensional lattice of trapped ion in the anti-nodes of this standing

wave. In the process of mechanical oscillations the position of ions relative the center of

anti-nodes are possible. In this case all information about this oscillation can be obtained

measuring the distances between the Mollow triplet peaks of resonance fluorescence. The in-

phase and anti-phase oscillations of this ion array is studied trough the interferences of resonance

fluorescent light from this system of radiators.

References

[1] N A Enaki and Yu M Shvera Opt. Spectrosc. 65 272(1988)

[2] N A Enaki , N Ciobanu and M Orszag , J. Phys. B: At. Mol. Opt. Phys. 44 (2011)

High-Fidelity Atom-Photon Entangling Operation

Yuuki Tokunaga1,2 1. NTT Secure Platform Laboratories, NTT Corporation, 3-9-11 Midori-cho, Musashino, Tokyo 180-8585, Japan

Tel: +81-422-59-3632, FAX: +81-422-59-3285, E-mail: [email protected] 2. Japan Science and Technology Agency, CREST, 5 Sanban-cho, Chiyoda-ku, Tokyo 102-0075, Japan

Abstract: We present a high-fidelity maximally entangling gate between an atom and a photon

using a three-level system with reflection geometry, where the dominant physical

imperfections are mapped into heralded losses instead of infidelities.

Entangling operation (EO) between atoms and photons is a key technology for realizing quantum information

processing. High-fidelity EO will enable us to make reliable long-range entanglement requisite for quantum

networks and distributed quantum computation [1]. Many researches on the EO using cavity QED systems have

been done so far. A major approach of them has been to aim the strong coupling regime for obtaining high-

fidelity EO such as [2]. However, experimentally realizing the strong coupling regime in cavity QED system is

still difficult task. On the other hand, recently, an alternative approach, so-called the Purcell regime or bad cavity regime, where the cavity-atom coupling is weaker than the cavity decay, is attracted attention because this is less

technically demanding and still gives us useful interactions [3-5]. Such proposals are promising for realizing key

components of quantum information processing, however, there still inherently exist physical imperfections, and

which should be eliminated to achieve the extremely small infidelity requirement (10-3

-10-2

) for fault-tolerant

processing [6,7]. Recently, Li et al. showed an idea to lessen infidelities for an entangling gate using a four-level

emitter with transmission and reflection geometry [8].

In this work, we present a high-fidelity maximally entangling gate between an atom and a photon for a three-

level system with reflection geometry. Our method basically exploits a model of system investigated in [4]

and we implement an error-detection mechanism, where the dominant physical imperfections are mapped into

heralded losses instead of infidelities.

In Fig. 1, we describe our scheme for high-fidelity atom-photon entangling operation. The atom has two

degenerate ground states , , and an excited state . The transitions and are assisted

by horizontally and vertically polarized photons, respectively. Radiative decay rates for the and

transitions are and . The atom is initialized to be in . First, the polarizing beam splitter (PBS)

spatially splits and components of an arbitrary incident single-photon. Here, for example, we use an

input . The component transmits the PBS1 and interacts with the atom, inducing SWAP

operation [4]

,

when the process is ideal. After reflection from the cavity, the correct component reflects at PBS1, then is

rotated to by half wave plate (HWP), and rejoins with the other component at PBS2. The ideal process

finally gives a maximally entangling operation and the state results in an entangled state

Owing to the imperfect atom-photon interaction process, the component may come out from the cavity, but

which transmits the PBS1 and results in a loss. The waveform corrector (WFC) in Fig. 1 compensates the spatial

wave functions of the packets. It may include an attenuator, a delay line, a phase modulator and such to make the

waveform coincide with the packet from the cavity. If the photon pulse length is sufficiently long and the

bandwidth is much smaller than the cavity decay rate, then the packet from the cavity will leave the pulse shape

almost unchanged and only attenuate. Otherwise, the pulse shape should also be compensated. Such a WFC

could be realized, for example, by another cavity setup where a two-level system absorbs and reemits the photon

in a similar radiative condition without making entanglement with it.

Next, we investigate the imperfection in more detail. In the case that the pulse length is sufficiently long as

, the four basis states are transformed on reflection as follows [4]:

,

,

where is the detuning of the input photon. When the input photon is in resonance with the atom ( ) and

, this gate behaves as an atom-photon SWAP gate. The difference between and induces the error of

the SWAP gate. Moreover, if the pulse length is not sufficiently long, then it also deteriorates the fidelity.

Therefore, the discrepancy between and and the finite pulse lengths are the main causes for degrading the

gate fidelity (See Fig.3 in [4], which shows contour plots of the gate fidelities as functions of these parameters).

In our scheme, such main errors are detected as a loss, (The WFC can also help to reduce the infidelity), and a

high-fidelity can be obtained when the photon comes to the correct output mode.

In summary, we have presented a high-fidelity maximally entangling gate between an atom and a photon

using a three-level system with reflection geometry. The dominant physical imperfections are mapped into

heralded losses instead of infidelities. This scheme can be used for generating a high-fidelity multi-partite

entanglement and would be useful for quantum information processing.

Fig.1. The schematic diagram of the setup.

References [1] H. J. Kimble, The quantum internet , Nature 453, 1023 (2008).

[2] J. Cirac, P. Zoller, H. Kimble, and H. Mabuchi, Quantum State Transfer and Entanglement Distribution among Distant Nodes in a

Quantum Network , Phys. Rev. Lett. 78, 3221 (1997).

[3] E. Waks and J. Vuckovic, Dipole Induced Transparency in Drop-Filter Cavity-Waveguide Systems , Phys. Rev. Lett. 96, 153601 (2006).

[4] K. Koshino, S. Ishizaka, and Y. Nakamura, Deterministic photon-photon SWAP gate using a system , Phys. Rev. A 82, 010301(R)

(2010).

[5] C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, CNOT and Bell-state analysis in the weak-coupling cavity QED regime , Phys. Rev. Lett. 104, 160503 (2010).

[6] R. Raussendorf and J. Harrington, Fault tolerant quantum computation with high threshold in two dimensions , Phys. Rev. Lett. 98,

190504 (2007). R. Raussendorf, J. Harrington, and K. Goyal, Topological fault-tolerance in cluster state quantum computation , New J. Phys. 9, 199 (2007).

[7] K. Fujii and Y. Tokunaga, Fault-Tolerant Topological One-Way Quantum Computation with Probabilistic Two-Qubit Gates , Phys. Rev.

Lett. 105, 250503 (2010). Y. Li, S. Barrett, T. Stace, and S. Benjamin, Fault Tolerant Quantum Computation with Nondeterministic Gates , Phys. Rev. Lett. 105, 250502 (2010).

[8] Y. Li, L. Aolita, D. Chang, and L. Kwek, Robust-Fidelity Atom-Photon Entangling Gates in the Weak-Coupling Regime Phys. Rev.

Lett. 109, 160504 (2012).

coupling cold atoms to nanophotonics: a novel platform for ......1 vladimir state university named...

Documents