Quantum coherence and interactions in many body systems

Collaborators:Ehud Altman, Anton Burkov, Derrick Chang, Adilet Imambekov, Vladimir Gritsev , Mikhail Lukin, Giovanna Morigi, Anatoli Polkonikov

Eugene Demler Harvard University

Funded by NSF, AFOSR, Harvard-MIT CUA

Condensed matter physics

Atomic physics

Quantum optics

Quantumcoherence

Quantuminformation

Quantum Optics with atoms andCondensed Matter Physics with photons

Interference of fluctuating condensatesFrom reduced contrast of fringes to correlation functionsDistribution function of fringe contrastNon-equilibrium dynamics probed in interference experiments

Luttinger liquid of photonsCan we get “fermionization” of photons?Non-equilibrium coherent dynamics of strongly interacting photons

Interference experimentswith cold atoms

Interference of independent condensates

Experiments: Andrews et al., Science 275:637 (1997)

Theory: Javanainen, Yoo, PRL 76:161 (1996)Cirac, Zoller, et al. PRA 54:R3714 (1996)Castin, Dalibard, PRA 55:4330 (1997)and many more

Interference of two independent condensates

1

2

r

r+d

d

r’

Clouds 1 and 2 do not have a well defined phase difference.However each individual measurement shows an interference pattern

Nature 4877:255 (1963)

Interference of one dimensional condensatesExperiments: Schmiedmayer et al., Nature Physics (2005,2006)

Transverse imaging

long. imaging

trans.imaging

Longitudial imaging

Figures courtesy of J. Schmiedmayer

x1

d

Amplitude of interference fringes,

Interference of one dimensional condensates

For identical condensates

Instantaneous correlation function

For independent condensates Afr is finite but is random

x2

Polkovnikov, Altman, Demler, PNAS 103:6125 (2006)

Interference of two dimensional condensates

Ly

Lx

Lx

Experiments: Hadzibabic et al. Nature (2006)

Probe beam parallel to the plane of the condensates

Gati et al., PRL (2006)

Interference of two dimensional condensates.Quasi long range order and the KT transition

Ly

Lx

Below KT transitionAbove KT transition

x

z

Time of

flight

low temperature higher temperature

Typical interference patterns

Experiments with 2D Bose gasHadzibabic, Dalibard et al., Nature 441:1118 (2006)

integration

over x axis

Dx

z

z

integration

over x axisz

x

integration distance Dx

(pixels)

Contrast afterintegration

0.4

0.2

00 10 20 30

middle Tlow T

high T

integration

over x axis z

Experiments with 2D Bose gasHadzibabic et al., Nature 441:1118 (2006)

fit by:

integration distance Dx

Inte

grat

ed c

ontr

ast 0.4

0.2

00 10 20 30

low Tmiddle T

high T

if g1(r) decays exponentially with :

if g1(r) decays algebraically or exponentially with a large :

Exponent

central contrast

0.5

0 0.1 0.2 0.3

0.4

0.3high T low T

2

21

2 1~),0(

1~

x

D

x Ddxxg

DC

x

“Sudden” jump!?

Experiments with 2D Bose gasHadzibabic et al., Nature 441:1118 (2006)

Fundamental noise in interference experiments

Amplitude of interference fringes is a quantum operator. The measured value of the amplitude will fluctuate from shot to shot. We want to characterize not only the averagebut the fluctuations as well.

Shot noise in interference experiments

Interference with a finite number of atoms. How well can one measure the amplitude of interference fringes in a single shot?

One atom: NoVery many atoms: ExactlyFinite number of atoms: ?

Consider higher moments of the interference fringe amplitude

, , and so on

Obtain the entire distribution function of

Shot noise in interference experiments

Interference of two condensates with 100 atoms in each cloud

Coherent states

Number states

Polkovnikov, Europhys. Lett. 78:10006 (1997)Imambekov, Gritsev, Demler, 2006 Varenna lecture notes

Distribution function of fringe amplitudes for interference of fluctuating condensates

L is a quantum operator. The measured value of will fluctuate from shot to shot.

Higher moments reflect higher order correlation functions

Gritsev, Altman, Demler, Polkovnikov, Nature Physics (2006)Imambekov, Gritsev, Demler, cond-mat/0612011

We need the full distribution function of

0 1 2 3 4

Pro

babi

lity

P(x

)

x

K=1 K=1.5 K=3 K=5

Interference of 1d condensates at T=0. Distribution function of the fringe contrast

Narrow distributionfor .Approaches Gumbeldistribution.

Width

Wide Poissoniandistribution for

Interference of 1d condensates at finite temperature.

Distribution function of the fringe contrast

Luttinger parameter K=5

Experiments: Schmiedmayer et al.

Interference of 2d condensates at finite temperature.

Distribution function of the fringe contrast

T=TKT

T=2/3 TKT

T=2/5 TKT

From visibility of interference fringes to other problems in physics

Quantum impurity problem: interacting one dimensionalelectrons scattered on an impurity

Conformal field theories with negative central charges: 2D quantum gravity, non-intersecting loop model, growth of random fractal stochastic interface, high energy limit of multicolor QCD, …

Interference between interacting 1d Bose liquids.Distribution function of the interference amplitude

is a quantum operator. The measured value of will fluctuate from shot to shot.How to predict the distribution function of

Yang-Lee singularity

2D quantum gravity,non-intersecting loops

Fringe visibility and statistics of random surfaces

)(h

Proof of the Gumbel distribution of interfernece fringe amplitude for 1d weakly interacting bosons relied on the known relation between 1/f Noise and Extreme Value StatisticsT.Antal et al. Phys.Rev.Lett. 87, 240601(2001)

Fringe visibility

Roughness dh2

)(

Non-equilibrium coherentdynamics of low dimensional Bose

gases probed in interference experiments

Studying dynamics using interference experiments.Thermal decoherence

Prepare a system by splitting one condensate

Take to the regime of zero tunneling Measure time evolution

of fringe amplitudes

Relative phase dynamics

Quantum regime

1D systems

2D systems

Classical regime

1D systems

2D systems

Burkov, Lukin, Demler, cond-mat/0701058

Experiments: Schmiedmayer et al.

Different from the earlier theoretical work based on a single mode approximation, e.g. Gardiner and Zoller, Leggett

Quantum dynamics of coupled condensates. Studying Sine-Gordon model in interference experiments

J

Prepare a system by splitting one condensate

Take to the regime of finitetunneling. Systemdescribed by the quantum Sine-Gordon model

Measure time evolutionof fringe amplitudes

Dynamics of quantum sine-Gordon model

Power spectrum

Gritsev, Demler, Lukin, Polkovnikov, cond-mat/0702343

A combination ofbroad featuresand sharp peaks.Sharp peaks dueto collective many-bodyexcitations: breathers

Condensed matter physics with photons

Luttinger liquid of photons

Tonks gas of photons:photon “fermionization”

Chang, Demler, Gritsev, Lukin, Morigi, unpublished

Self-interaction effects for one-dimensional optical waves

kk0

Nonlinear polarization for isotropic medium

Envelope function

Self-interaction effects for one-dimensional optical waves

Frame of reference moving with the group velocity

Gross-Pitaevskii type equation for light propagation

Competition of dispersion and non-linearity

Nonlinear Optics, Mills

Self-interaction effects for one-dimensional optical waves

BEFORE: two level systems and insufficient mode confinement

Interaction corresponds to attraction.Physics of solitons (e.g. Drummond)

Weak non-linearity due to insufficient mode confining

Limit on non-linearity due to photon decay

NOW: EIT and tight mode confinement

Sign of the interaction can be tuned

Tight confinement of theelectromagnetic modeenhances nonlinearity

Strong non-linearity without lossescan be achieved using EIT

Controlling self-interaction effects for photons

c

Imamoglu et al.,PRL 79:1467 (1997)

describes photons. We need to normalize to polaritons

Tonks gas of photons

Photon fermionization

Crystal of photons

Is it realistic?Experimental signatures

Tonks gas of atoms

Small – weakly interacting Bose gas

Large – Tonks gas. Fermionized bosons

Additional effects for for photons: Photons are moving with the group velocity Limit on the cross section of photon interacting with one atom

Tonks gas of photons

Limit on strongly interacting 1d photon liquid due to finite group velocity

Concrete example: atoms in a hollow fiber

Experiments: Cornell et al. PRL 75:3253 (1995);Lukin, Vuletic, Zibrov et.al.

Theory: photonic crystal and non-linear mediumDeutsch et al., PRA 52:1394 (2005);Pritchard et al., cond-mat/0607277

Atoms in a hollow fiber

k

Without using the “slow light” points

=1mA=10m2

Ltot=1cm

A – cross section of e-m mode

Typical numbers

Experimental detection of the Luttinger liquid of photons

Control beam off.Coherent pulse of non-interacting photons enters the fiber.

Control beam switched on adiabatically.Converts the pulse into a Luttinger liquidof photons.

“Fermionization” of photons detected by observing oscillations in g2

c

K – Luttinger parameter

Non-equilibrium dynamics of strongly correlated many-body systems

g2 for expanding Tonks gas with

adiabatic switching of interactions

100 photons after expansion

Outlook

Atomic physics and quantum optics traditionally study non-equilibrium coherent quantum dynamics of relatively simple systems.

Condensed matter physics analyzes complicated electron systembut focuses on the ground state and small excitations around it.

We will need the expertise of both fields

Next challenge in studying quantum coherence:understand non-equilibrium coherent quantum dynamics of strongly correlated many-body systems

“…The primary objective of the JQI is to develop a world class research institute that will explore coherent quantum phenomena and thereby lay the foundation for engineering and controlling complex quantum systems…”

From the JQI web page http://jqi.umd.edu/