Spontaneous crystallization of light and ultracold atoms

Helmut RitschTheoretische Physik

Universität Innsbruck

QLIGHTCRETE, Kreta, June 2016

COST MP1403

NANOSCALE

QUANTUM

OPTICS

Claudiu Genes

Francesco Piazza

PostDocs‘s :

Tobias Griesser

Wolfgang Niedenzu

Ph.D‘s

Laurin Ostermann

Raimar Sandner

Sebastian Krämer

Stefan Ostermann

Dominik Winterauer

Valentin Torggler

Daniela Holzmann

David Plankensteiner

Master students:

Philipp Aumann

Collaborations (theory):

Peter Domokos, Andras Vukics, Janos Asboth (Budapest)

Giovanna Morigi (Saarbrücken), Aurelian Dantan (Aarhus)

Igor Mekhov (Oxford), David Vitali (Camerino), Hashem Zoubi (Hannover),

M. Holland, J. Schachenmayer (JILA, Boulder)

People

• Collective scattering, self-ordering and quantum simulationin optical resonators

• Ordering forces in confined 1D optical structures

• Atom light crystallizationof an laser illuminated ultra-cold gas

Ultracold gases: quantum particles

in

optical potentials

Quantum optics:dynamics

of

quantized light modes

Quantum optics with quantum gases:

full quantum dynamics of light and matter waves

in

dispersive (non-resonant) regime

light induces a quantized optical potential

+

atoms generate a quantum refractive index

Basic Physics

H. R., P Domokos, F. Brennecke, T. Esslinger, Rev. Mod. Phys., 2013

Part I:

collective scattering

and self-ordering in

resonators

U(x) = optical potential / photon =

cavity frequency shift / atom

atom-field interaction via optical potential U

dipole force dominates radiation pressure

U >> k >> g single atom shifts cavity in or out of resonance

single photon creates an optical trap for an atom

g(x) = photon loss / atom =

radiation pressure / photon

go … coupling strength

g … atomic width

k ... cavity linewidth

Dispersive Cavity QED

for matter waves:

∆𝒂 = 𝝎𝒍𝒂𝒔𝒆𝒓 −𝝎𝒂𝒕𝒐𝒎 ≫ g𝒂𝒕𝒐𝒎

Strong coupling re-defined

Ultrastrong coupling

U >> Dwmode >> k

U >> g

single mode picture breaks down

nonlinear coupled multi mode model

Dispersive limit Da >> g

U,g

U = g2/Da g = G g2/Da2

Ultracold gas near T= 0 in a quantum optical lattice potential

n=4

n=3

n=2

Atomic quantum dynamics in cavities

effective single atom Hamiltonian

U x g kxa

a

( ): cos ( )

D

D2

0

2 0

2 2

g

gg

g( ): cos ( )x g kx

a

0

2

0

2 0

2 2

D

>

Looks similar to standard Bose Hubbard model

but

“parameters” for lattice dynamics are field operators

Hubbard model

for a quantized single mode

bosons in thermodynamic limit:

M. Lewenstein, G. Morigi et. al. (PRL 2007,2008)

generalization to fermions:

Morigi PRA 2008

Cavity creates extra effective long range attraction or repulsion

=> parameter regions with two stable phases

=> phase „superpositions“ of Mott insulator + superfluid ?

recall: phases of cavity generated lattices in thermodynamic limit

Crystallisation of particles

through

superradiant scattering

z

x

x

phase of scattered light

depends on position x,z

collective pump strength R

Field in cavity generated only by atoms

R = 0 for random atomic distribution

R ~ Ng for regular lattice (Bragg)

transverse laser pump:

direct excitation of

atoms from side !

Maximum photon number for 0 and l distance

Minimum photon number for l/2 distance

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0

1

2

3

4

x 10-3

x-Atom1

cavity field intensity

x-Atom2

Two scatterers placed along cavity axis

Cavity field as a function of atom position

laser

x1 x2

l ordering give maximal field

for high field seekers

ordering is energetically favourable

forces on 2 atoms in cavity 2 Hopfield „neurons“

cavity field creates optical forces

atoms drawn towards antinodes

where scattering is maximized !

Numerical simulations of coupled atom field dynamics

cavity axis

pum

p a

xis

• particles spontaneously form crystalline order

• Bragg scattering creates N^2 `superradiance‘

2D - particle motion

starting from random distribution

Selforganisation as an open system phase transition

critical point

Selfconsistent atom-field distribution

even sites

odd sites

pump power

Atom-field dynamics for large ensembles: => Vlasov-Maxwell equations (see G. Robb, M. Hemmerling)

Continuous density model for atoms

single particle distribution function

Vlasov + Maxwell equations

cavity

damping

pump laser

opt. potential

frequency

shift of cavity

ordering threshold at thermal equilibrium

phase diagram including diffusion

Niedenzu, EPL 2011

temperature

mean field optical potential

Selforganization of a BEC at T ~ 0 (mean field)

Nagy, Domokos, PRL (2010), NJP 2011

Fernandez-Vidal, Morigi PRA (2010)

Zwerger, Piazza …

Two-mode BEC approximation

=> Tavis-Cummings model

BEC

„Dicke Superradiant Phase“ transition

(predicted by Hepp+Lieb 1973)

threshold from quantum fluctuations

K Baumann et al. Nature 464, (2010)

• pump creates optical lattice with

atoms in lowest band

• cavity field from scattered lattice light

Effective Hubbard type Hamiltonian:

pump amplitude determined by atomic distribution operator

multiparticle quantum description of selforganization in a lattice

Selfordering beyond mean field

older work;

M. Lewenstein, G. Morigi et.al. PRL 2007, 2008

full quantum regime (BH): self ordering phase transition in optical lattice

W. Hofstetter (2010)

R. Bakhtiari, M. Thorwart, HR (2014)

G. Morigi, 2016

R. Landig et. al, Nature 533, 2016

A. Hemmerich et.al., PRL 2016

Experiments:

ETH

( + Hamburg )

intermediate phase with

coherence + diagonal order => supersolid

Theory

DMFT-calculation

Selfordering in laser fields with several distinct frequencies

single frequency (mode 5) three colors (mode 2+3+4)

x2

x1

x2

At some positions particles scatter all colorsx1

Field amplitudes:

Forces and fields for two particles

Equilibrium positions = positions with high scattering intensity

Particles tend to stay close to positions

of optimum scattering and trapping:

adaptive „light collection“ system

system „learns“ in time

memorizes previous conditions

Particle field dynamics with (quantum) noise:

guided Brownian motion

Quasi-random walk

between high scattering areasTime averaged

position distribution

system optimizes

scattering and „learns“

from the past

Adaptive + learning light collection system

Sum of order parameters:

Alternative: „disspative“ annealing

turn on 2.+ 9. mode illumination

fast switch slow switch

system converges mostly to optimal states for both modes

Selfordering with multicolor pump at T=0 :

=> competitive quantum phase transitions

multimode Tavis Cummings model

Nonlinear coupled oscillator model

with tailorable coupling:

pump amplitudes + detunings as control

Interacting trapped quantum particles within a multimode cavity

Particle-field

Hamiltonian

coupling

vectors

Effective Hamiltonian after field elimination

yes, we can engineer coupling matrices Aij by choice of modes + pumps !

Example: implementation of „Hopfield model, associative memory“

energy spectrum

searched pattern is lowest energy state

single occupations

per site

Example: 10 sites

(„Hopfield model – associative memory“)

state converges to searched pattern

Is this a general purpose quantum simulator ??

fast switch slow switch

C. Noh + DG Angelakis, arXiv:1604.04433v1JI. Cirac + P. Zoller, Nat. Phys, 8:264, 2012.

Part II :

collective scattering

in confined geometry

in 1D

(no mirrors)

waveguide nanostructure

D. Chang, I. Cirac et. al., PRL13

J. Kimble + more

Idea:transverse illumination induces scatterers to self arrange in ordered structure

induced by collective scattering => scattering model description

tapered fiber

A. Rauschenbeutel, E. Polzik

S. NicChormaic

Light induced interaction via collective scattering

into waveguide

(+ forces along a 1D trap)

tapered fiber + chip

S. Rolston, L. Orosco

microscopic dynamic model of scattering and forces near fiber :

--> scattering matrix approach

A C

DB

A C

DB

A C

DB

A C

DB

single particle

close to fibre:particle chain: free propagation between scatteres

Force (Maxwell stress tensor)

field amplitudes

are linearly coupled:

1. multiply matrices

2. enforce correct boundary conditions

3. calculate fields + forces

4. Dynamics of particles

z

z zr i zi

M(z)

P

(Deutsch/Philipps 1995, Asboth 2005)

two particles = double slit

dynamic evolution negligible absorption

forces

dynamic evolution with strong absorption

* particles scatter collectively and order at ¾ l distance

* particles form a resonator and confine light

many particles dynamics:

collective scattering, forces and friction

outer particles act as Bragg mirrors and trap inner particles

=> system forms a self organized optical resonator

T. Griesser, PRL 2013

( Vlasov approach)

Coupled equations for field E(z) :Helmholtz

and

spatial distribution f(z): Vlasov -Boltzmann

polarizability

densityeffective pump power

Instability of homogeneous order at e x >

Many particles: ultracold gas trapped along or within a fiber

(see also: Chang et.al , PRL 2013)

Atomic distribution

Field distribution

right

wave

left

running

selfconsistent atom-field solution for e x >

Outer particles act like mirrors to confine light and trap inner particles

! self odered cavity QED system !

band gap

Higher „order“ solutions for stronger pump

Particles generate a series of coupled cavities for light

=> engineering and optimization done by the system itself !

Part III :

free space

atom-light crystallization

An ultracold gas trapped in counterpropagating laser beams

fields have different frequency and/or polarization

to avoid spatial interference

=> translation invariant optical dipole trap

Gross Pitaevskii for cold gas

Maxwell / Helmholtz for fields

• gas constitutes dynamic refractive index:

• light creates dynamic optical potential:

‚dispersive‘ off resonant interaction :

density fluctuations and instability

in an optical dipole trap

weak dipole trap

„roton“ – instability (Kuritzky)

above critical laser power

density fluctuations => light fluctuations

=> more density fluctuationsordering instability

at critical wavevector

crystallization to ordered phase above threshold:

particle density = Bragg reflector

field intensities = optical lattice

the two fields are shifted:

=> aperiodic solution

ordering in an additional longitudinal trap

* atoms create confined light cavity

* light creates lattice trap for atoms

long range interaction and phonons

dynamics of peak densities

linearized perturbations:

phonon spectra :

infinite range interaction => phonon gap

solid state toy model with phonons at zero temperature

• Collective light scattering leads to crystallisation

of mobile particles in resonators, near fibres and even in free space

• Multiple frequencies enhance selfordering and coupling

=> self optimizing light collection system with memory

=> Hopfield memory model and quantum simulation

• Selfordering appears also in fibres with a continuum of light modes

with particles forming the resonators themselves

• Free space selfordering (optical binding) appears

also for point particles in broadband fields and blackbody radiation

Summary and Outlook

Thanks ! visitors welcome !

narrow band

radiation

black body

radiation

effective 2-body interaction

Ordering instabilityCollapse instability

• Gripped by light: optical binding,

K Dholakia, P Zemánek, Rev. Mod. Phys. 201

• Superdiffusion in optically controlled active media

A. Dogariu, Nature Photonics 6, 834–837 , (2012)

• Controlling dispersion forces between small particles

with artificially created random light fields,

F. Scheffold, JJ. Saenz (2015)

Light induced self-ordering in a 2D planar trap

with random or blackbody illumination

Interference of scattered fields and

incident fields creates

long range interaction

=> optical potential

single dipole field:

x

effective interaction

Instability condition:

X-polarized

plane wave

Pump

along z Random light fields:

Interaction potential strength

from collective scattering

x

y

σ = L/l

2D random distribution under transverse illumination exhibts density instability !

(like optical binding but with point dipoles+ random field)