Quantum coherence and interactions in many body systems

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Quantum coherence and interactions in many body
systems
Eugene Demler Harvard
University
Collaborators Ehud Altman, Anton Burkov, Derrick
Chang, Adilet Imambekov, Vladimir Gritsev ,
Mikhail Lukin, Giovanna Morigi, Anatoli
Polkonikov
Funded by NSF, AFOSR, Harvard-MIT CUA
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Condensed matter physics
Atomic physics
Quantum coherence
Quantum optics
Quantum information
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Quantum Optics with atoms andCondensed Matter
Physics with photons
Interference of fluctuating condensates From
reduced contrast of fringes to correlation
functions Distribution function of fringe
contrast Non-equilibrium dynamics probed in
interference experiments
Luttinger liquid of photons Can we get
fermionization of photons? Non-equilibrium
coherent dynamics of strongly interacting photons
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Interference experimentswith cold atoms
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Interference of independent condensates
Experiments Andrews et al., Science 275637
(1997)
Theory Javanainen, Yoo, PRL 76161
(1996) Cirac, Zoller, et al. PRA 54R3714
(1996) Castin, Dalibard, PRA 554330 (1997) and
many more
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Interference of two independent condensates
r
r
1
rd
d
2
Clouds 1 and 2 do not have a well defined phase
difference. However each individual measurement
shows an interference pattern
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Nature 4877255 (1963)
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Interference of one dimensional condensates
Experiments Schmiedmayer et al., Nature Physics
(2005,2006)
Transverse imaging
Longitudial imaging
Figures courtesy of J. Schmiedmayer
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Interference of one dimensional condensates
Polkovnikov, Altman, Demler, PNAS 1036125
(2006)
d
x1
For independent condensates Afr is finite but Df
is random
x2
Instantaneous correlation function
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Interference of two dimensional condensates
Experiments Hadzibabic et al. Nature (2006)
Gati et al., PRL (2006)
Probe beam parallel to the plane of the
condensates
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Interference of two dimensional
condensates.Quasi long range order and the KT
transition
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z
x
Typical interference patterns
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Experiments with 2D Bose gas
Hadzibabic et al., Nature 4411118 (2006)
x
integration over x axis
z
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Experiments with 2D Bose gas
Hadzibabic et al., Nature 4411118 (2006)
fit by
Integrated contrast
integration distance Dx
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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 average but the
fluctuations as well.
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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 No Very many
atoms Exactly Finite number of atoms ?
Consider higher moments of the interference
fringe amplitude
Obtain the entire distribution function of
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Shot noise in interference experiments
Polkovnikov, Europhys. Lett. 7810006
(1997) Imambekov, Gritsev, Demler, 2006 Varenna
lecture notes
Interference of two condensates with 100 atoms in
each cloud
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Distribution function of fringe amplitudes for
interference of fluctuating condensates
Gritsev, Altman, Demler, Polkovnikov, Nature
Physics (2006) Imambekov, Gritsev, Demler,
cond-mat/0612011
Higher moments reflect higher order correlation
functions
We need the full distribution function of

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Interference of 1d condensates at T0.
Distribution function of the fringe contrast
Narrow distribution for
. Approaches Gumbel distribution. Width
Wide Poissonian distribution for
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Interference of 1d condensates at finite
temperature. Distribution function of the
fringe contrast
Experiments Schmiedmayer et al.
Luttinger parameter K5
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Interference of 2d condensates at finite
temperature. Distribution function of the
fringe contrast
TTKT
T2/3 TKT
T2/5 TKT
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From visibility of interference fringes to other
problems in physics
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Interference between interacting 1d Bose
liquids. Distribution function of the
interference amplitude
Quantum impurity problem interacting one
dimensional electrons 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,

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Fringe visibility and statistics of random
surfaces
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)
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Non-equilibrium coherentdynamics of low
dimensional Bose gases probed in interference
experiments
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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
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Relative phase dynamics
Burkov, Lukin, Demler, cond-mat/0701058
Different from the earlier theoretical work based
on a single mode approximation, e.g. Gardiner
and Zoller, Leggett
Experiments Schmiedmayer et al.
1D systems
2D systems
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Quantum dynamics of coupled condensates.
Studying Sine-Gordon model in interference
experiments
Take to the regime of finite tunneling.
System described by the quantum Sine-Gordon model
Prepare a system by splitting one condensate
Measure time evolution of fringe amplitudes
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Dynamics of quantum sine-Gordon model
Gritsev, Demler, Lukin, Polkovnikov,
cond-mat/0702343
A combination of broad features and sharp
peaks. Sharp peaks due to collective
many-body excitations breathers
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Condensed matter physics with photons
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• Luttinger liquid of photons

Tonks gas of photons photon fermionization
Chang, Demler, Gritsev, Lukin, Morigi, unpublished
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Self-interaction effects for one-dimensional
optical waves
Nonlinear polarization for isotropic medium
Envelope function
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Self-interaction effects for one-dimensional
optical waves
Frame of reference moving with the group velocity
Gross-Pitaevskii type equation for light
propagation
Nonlinear Optics, Mills
Competition of dispersion and non-linearity
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Self-interaction effects for one-dimensional
optical waves
BEFORE two level systems and insufficient mode
confinement
NOW EIT and tight mode confinement
Interaction corresponds to attraction. Physics of
solitons (e.g. Drummond)
Sign of the interaction can be tuned
Tight confinement of the electromagnetic
mode enhances nonlinearity
Weak non-linearity due to insufficient mode
confining
Limit on non-linearity due to photon decay
Strong non-linearity without losses can be
achieved using EIT
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Controlling self-interaction effects for photons
D w
w
Wc
w
Imamoglu et al., PRL 791467 (1997)
describes photons. We need to normalize to
polaritons
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Tonks gas of photons
Photon fermionization
Crystal of photons
Is it realistic? Experimental signatures
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Tonks gas of atoms
Small g weakly interacting Bose gas
Large g 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
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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 753253
(1995) Lukin, Vuletic, Zibrov et.al.
Theory photonic crystal and non-linear
medium Deutsch et al., PRA 521394
(2005) Pritchard et al., cond-mat/0607277
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Atoms in a hollow fiber
A cross section of e-m mode
Typical numbers
l1mm A10mm2 Ltot1cm
Without using the slow light points
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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 liquid of photons.
Fermionization of photons detected by observing
oscillations in g2
K Luttinger parameter
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Non-equilibrium dynamics of strongly correlated
many-body systems
g2 for expanding Tonks gas with adiabatic
switching of interactions
100 photons after expansion
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Outlook
Next challenge in studying quantum
coherence understand non-equilibrium coherent
quantum dynamics of strongly correlated
many-body systems
Atomic physics and quantum optics traditionally
study non-equilibrium coherent quantum dynamics
of relatively simple systems.
Condensed matter physics analyzes complicated
electron system but focuses on the ground state
and small excitations around it.
We will need the expertise of both fields
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/