lphys’07 – leon – august 22 nd 2007 alessandro zavatta, valentina parigi, myungshik kim, and...

LPHYS’07 – Leon – August 22nd 2007LPHYS’07 – Leon – August 22nd 2007

Alessandro Zavatta, Valentina Parigi, Myungshik Kim,

and Marco Bellini Istituto Nazionale di Ottica Applicata (INOA) - CNR, Florence, Italy

LENS and Physics Dept., University of Florence, ItalySchool of Mathematics and Physics, The Queen’s University, Belfast, UK

Alessandro Zavatta, Valentina Parigi, Myungshik Kim,

and Marco Bellini Istituto Nazionale di Ottica Applicata (INOA) - CNR, Florence, Italy

LENS and Physics Dept., University of Florence, ItalySchool of Mathematics and Physics, The Queen’s University, Belfast, UK

Probing quantum commutation rules by adding and subtracting single photons

to/from a light field

Probing quantum commutation rules by adding and subtracting single photons

to/from a light field

Bled 26-28 Bled 26-28 MarchMarch 2008 2008

Dipartimento Dipartimento di Fisica di FisicaINOA-CNRINOA-CNR


OutlineOutline

Experimental implementation of photon creation Experimental implementation of photon creation and annihilation operatorsand annihilation operators

Application to a completely classical light fieldApplication to a completely classical light field

Nonclassical and counterintuitive featuresNonclassical and counterintuitive features

Direct probing of fundamental quantum rulesDirect probing of fundamental quantum rules



Implementing single-photon addition and subtraction

Implementing single-photon addition and subtraction

Use photon creation and Use photon creation and annihilation operatorsannihilation operators

“Photon-added” state“Photon-added” state

“Photon-subtracted” state“Photon-subtracted” state

Conditional generation schemesConditional generation schemes

Bled 26-28 Bled 26-28 MarchMarch 20082008


UseUse parametric down-parametric down-conversionconversion

in a nonlinear crystalin a nonlinear crystalStay in the low-gain regimeStay in the low-gain regime

(eliminates higher-order (eliminates higher-order excitations)excitations)

… whenever an idler photon is detected, the signal is prepared in a single-photon-

excited version of the initial stateStimulated emission Stimulated emission regimeregime

Emission probability increases with <n>Emission probability increases with <n>

| s|

i

|i a |+

s2

Adding a single photon to a light fieldAdding a single photon to a light field

Inject a seed pure state in the signal Inject a seed pure state in the signal modemode

Bled 26-28 Bled 26-28 MarchMarch 20082008A. Zavatta, S. Viciani, M. Bellini, Science 306, 660 (2004); Phys. Rev. A, 72, 023820 (2005)


(Pseudo-)thermal light source(Pseudo-)thermal light source

Rotating ground glass diskRotating ground glass disk

Diffuses the input coherent beam and adds random

amplitude and phase fluctuations


Single-mode fiberSingle-mode fiber


For a generic mixed input state and upon conditioning

on single idler photon detection

Mixed state inputMixed state input

1 2 3 4 5 6 7 8 9 10 11

0.1

0.2

0.3

0.4

0.5

The addition of a single photon turns any state into a nonclassical one due to the lack of the vacuum terms

C. T. Lee, Phys. Rev. A 52, 3374 (1995)

1 2 3 4 5 6 7 8 9 10 11

0.1

0.2

0.3

0.4

0.5

Thermal input state



Glauber-Sudarshan P distribution

Wigner distribution

Both distributions are Both distributions are always negative at the always negative at the

originorigin

Nonclassical statesNonclassical statesindependent of <n>independent of <n>

Nonclassicality of photon-added thermal statesNonclassicality of photon-added thermal states



Experimental single-photon additionExperimental single-photon addition



Pθ(x

θ)

xθ

Complete set of quadrature

distributions

Complete set of quadrature

distributions

• Gated time-domain acquisition

• Ultra-high bandwidth (~100

MHz)

• Low electronic noise (S/N >12

dB)

• High subtraction efficiency

(~60 dB @ 82 MHz)

Ultrafast homodyne detectionUltrafast homodyne detection

Density matrix elements

Density matrix elements

nm

Wigner function

Wigner function

Maximum likelihood estimation

A. I. Lvovsky, J. Opt. B: Quantum Semiclassical Opt. 6, 556 (2004)Z. Hradil, D. Mogilevtsev, J. Rehacek, Phys. Rev. Lett. 96, 230401 (2006)


A. Zavatta, M. Bellini, P.L. Ramazza, F. Marin, F.T. Arecchi, J. Opt. Soc. Am. B 19, 1189 (2001).


n=1.15n=1.15__

n=0.1n=0.1__

Thermal statesThermal states Single-photon-added thermal states

Single-photon-added thermal states

Experimental tomographic reconstructionExperimental tomographic reconstruction

Adding a photon makes the states highly nonclassical. Their Wigner function becomes negative at the origin

No correction for the finite homodyne detection efficiency


A. Zavatta, V. Parigi, M. Bellini, Phys. Rev. A 75, 052106 (2007)


The experimental inefficiency in the preparation and detection can be simply introduced as a loss by a BS of transmittivity .

Both the finite efficiency and the statistical noise contribute to reduce the visibility of nonclassical features.

Wigner negativity and efficienciesWigner negativity and efficiencies

Fock statesFock states

Bled 26-28 Bled 26-28 MarchMarch 20082008A. Zavatta, V. Parigi, M. Bellini, Phys. Rev. A 75, 052106 (2007)


How to subtract a single photon ?How to subtract a single photon ?


On/off detection

Input state


Experimental single-photon subtractionExperimental single-photon subtraction

Bled 26-28 Bled 26-28 MarchMarch 20082008J. Wenger, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 92, 153601 (2004)


Subtracting a single photon from a thermal light state preserves its classicality but changes the Wigner function to a non-Gaussian one.

n=0.5n=0.5__

n=1.0n=1.0__

Thermal statesThermal states Photon-subtracted thermal states

Photon-subtracted thermal states

Tomographic reconstructionsTomographic reconstructions



n=0.5n=0.5__

n=1.0n=1.0__

Thermal statesThermal states Photon-subtracted thermal states

Photon-subtracted thermal states

nsub=0.7nsub=0.7__

n sub=1.3n sub=1.3__

n=0.33n=0.33__

n=0.65n=0.65__

Mean photon numbersMean photon numbers

The mean number of photons in the state increases after photon subtraction !!!



for a coherent statennsub

for a Fock state1nnsub

for a thermal state nnsub 2

Fnnsub 1

n

nF

2)(

Subtracting a single photon from a state may increase the resulting mean photon number if the initial state was super-

Poissonian.

where

Fano parameterFano parameter

!!!!!!

The strange case of photon subtractionThe strange case of photon subtraction

Photon creation and annihilation operators do not performdeterministic photon addition and subtraction !

M. Ueda, N. Imoto, T. Ogawa, Phys. Rev. A 41, 3891 (1990) Bled 26-28 Bled 26-28 MarchMarch 20082008


Combining quantum operatorsCombining quantum operators



Experimental sequences of single-photon addition and subtraction

Experimental sequences of single-photon addition and subtraction



Directly probing quantum commutation rulesDirectly probing quantum commutation rules

Direct test of quantum commutation rules

Contrary to naïve classical expectations, “adding” and then “subtracting” a single photon modifies the state



Homodyne data and reconstructionsHomodyne data and reconstructions

Reconstructions corrected for the finite

detection efficiency (=64%)

Limited preparation efficiency (=92%) in the

photon-addition stage adds small contaminations

n

nn

21

661 2

n

nn

21

)32(2

n

n2

12 n

Clearly different final states



Experimental Wigner functionsExperimental Wigner functions

Nonclassical:negative WFNonclassical

but positive WFV. Parigi, A. Zavatta, M. S. Kim, M. Bellini, Science 317, 1890 (2007)



ConclusionsConclusions

First implementation of sequences of basic quantum First implementation of sequences of basic quantum operatorsoperators

Direct test of fundamental quantum algebraic rules: Direct test of fundamental quantum algebraic rules: noncommutativity of creation and annihilation noncommutativity of creation and annihilation

operatorsoperators

Nonclassical Multi-photon state generation through Nonclassical Multi-photon state generation through enhancement cavityenhancement cavity


Generation of SPATS and P-function reconstructionGeneration of SPATS and P-function reconstruction


Florence Quantum optics GroupFlorence Quantum optics Group


[email protected]

www.inoa.it/home/QOG

[email protected]

www.inoa.it/home/QOG

lphys’07 – leon – august 22 nd 2007 alessandro zavatta, valentina parigi, myungshik kim, and...

Documents