Interference experiments with ultracold atoms

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Interference experiments with ultracold atoms
Eugene Demler Harvard
University
Collaborators Ehud Altman, Anton Burkov, Robert
Cherng, Adilet Imambekov, Serena
Fagnocchi, Vladimir Gritsev, Mikhail Lukin, David
Pekker, Anatoli Polkovnikov
Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA,
MURI
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Outline
Introduction. Interference of fluctuating low
dimensional condensates. Systems of mixed
dimensionality Interference of fermions probing
paired states Detection of s-wave
pairing Detection of FFLO Detection of d-wave
pairing Interference experiments and
non-equilibrium dynamics Decoherence of uniformly
split condensates Ramsey interference of one
dimensional systems Splitting condensates on
Y-junctions
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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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z
x
Experiments with 1D Bose gas

Hofferberth et al. arXiv0710.1575
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Interference of fluctuating condensates
Polkovnikov, Altman, Demler, PNAS 1036125(2006)
x1
For independent condensates Afr is finite but Df
is random
L
x2
Instantaneous correlation function
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Interference between fluctuating condensates
high T
BKT
Time of flight
low T
2d BKT transition, Hadzibabic et al, 2006
1d Luttinger liquid, Hofferberth et al., 2007
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Distribution function of interference fringe
contrast
Experiments Hofferberth et al.,
arXiv0710.1575 Theory Imambekov et al. ,
cond-mat/0612011
Quantum fluctuations dominate asymetric Gumbel
distribution (low temp. T or short length L)
Thermal fluctuations dominate broad Poissonian
distribution (high temp. T or long length L)
Intermediate regime double peak structure
Comparison of theory and experiments no free
parameters Higher order correlation functions can
be obtained
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Systems of mixed dimensionality Weakly
coupled 2D condensates
Experiments M. Kasevich et al.,
Interplay of two dimensional physics of the BKT
transition and coupling along the 3rd direction
Connection to quasi-2D and 1D condensed matter
systems quantum magnets, organic
superconductors, high Tc cuprates, and many more
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Berezinskii Kosterlitz Thouless transition
Fisher Hohenberg, PRB 37, 4936 (1988)
TTBKT
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Temperature scales for weakly coupled pancakes
3D Phonons
TTC
TTBKT
3D XY
temperature
T2t
T0
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Interference of a stack of coupled pancakes
Pekker, Gritsev, Demler
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Interference experiments with fermionsprobing
paired states
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Interference of fermionic systems
A pair of independent fermionic systems

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Interference as a probe of fermionic pairing
Pairing correlations
Expectation value vanishes for independent
systems due to random relative phase between D1
and D2
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Interference as a probe of pairing
Polkovnikov, Gritsev, Demler
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FFLO phase
Pairing at finite center of mass momentum
Theory Fulde, Ferrell (1964) Larkin,
Ovchinnikov (1965) Bowers, Rajagopal (2002)
Liu, Wilczek (2003) Sheehy, Radzihovsky (2006)
Combescot (2006) Yang, Sachdev (2006) Pieri,
Srinati (2006) Parish et al., (2007) and many
others Experiments
Zwierlein, Ketterle et al., (2006)
Hulet et al., (2006)
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Interference as a probe of FFLO phase
Manual integration
Integration by a laser beam
x
y
when q matches one of the wavevectors of D(r) of
FFLO phase
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d-wave pairing
Fermionic Hubbard model
Possible phase diagram of the Hubbard
model D.J.Scalapino Phys. Rep. 250329 (1995)
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Phase sensitive probe of d-wave pairing in high
Tc superconductors
Superconducting quantum interference device
(SQUID)
Van Harlingen, Leggett et al, PRL 712134 (93)
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Other signatures of d-wave pairing dispersion
of quasiparticles
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Superconducting gap


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Quasiparticle energies
Low energy quasiparticles correspond to four
Dirac nodes

• Observed in
• Photoemission
• Raman spectroscopy
• T-dependence of thermodynamic
• and transport properties, cV, k, lL
• STM
• and many other probes

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Phase sensitive probe of d-wave pairing in high
Tc superconductors
Superconducting quantum interference device
(SQUID)
Van Harlingen, Leggett et al, PRL 712134 (93)
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Interference as a probe of d-wave pairing
d-wave superfluid
s-wave superfluid
System 1 is an s-wave superfluid System 2 is a
d-wave superfluid Regions II and III differ only
by 90o rotation
Phase sensitive probe of d-wave pairing
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Interference experiments and non-equilibrium
dynamics
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Uniform splitting of the condensates
Prepare a system by splitting one condensate
Take to the regime of zero tunneling
Measure time evolution of fringe amplitudes
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Long phase coherence implies squeezing factor of
10. Squeezing due to finite time of splitting.
Leggett, Sols, PRL (1998)

Burkov et al., PRL (2007)
Squeezing factor
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1d BEC Decay of coherence Experiments
Hofferberth, Schumm, Schmiedmayer, Nature (2007)
double logarithmic plot of the coherence
factor slopes 0.64 0.08 0.67 0.1 0.64
0.06
T5 110 21 nK T10 130 25 nK T15 170 22
nK
get t0 from fit with fixed slope 2/3 and
calculate T from
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Relative phase dynamics beyond single mode
approximation
Hamiltonian can be diagonalized in momentum space
Initial state fq 0
Conjugate variables
Need to solve dynamics of harmonic oscillators
at finite T
Coherence
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Relative phase dynamics beyond single mode
approximation
Bistritzer, Altman, PNAS (2007) Burkov, Lukin,
Demler, PRL (2007)
1D systems
2D systems
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Dynamics of condensate splittingand Ramsey
interference
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Ramsey interference
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Interaction induced collapse of Ramsey fringes
Experiments in 1d tubes A. Widera, et al. arXiv
07092094
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Spin echo. Time reversal experiments
Single mode approximation predicts full revival

• Experiments in 1d tubes
• Widera, et al. arXiv 07092094.
• Need to analyze multi-mode model in 1d
• Only q0 mode shows complete spin echo
• Finite q modes continue decay
• The net visibility is a result of competition
• between q0 and other modes

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Splitting condensates on Y-junctions quantum
zipper problem
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Splitting condensates on Y-junctions
Partial splitting stage new physics
Full splitting stage same as before
Earlier work Non-interacting atoms Scully and
Dowling, PRA (1993) Analysis of transverse modes
Jaasekelatnen and Stenholm, PRA
(2003) Tonks-Girardeau regime Girardeau et al.
PRA (2002)
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Splitting condensates on Y-junctions
beyond mean-field
1st arm
2nd arm
Wave equation in both arms of the interferometer.
c is the speed of sound
Time dependent boundary conditions in the frame
of the condensate. v is the condensate velocity
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Moving mirror problem in optics
Moore, J. Math. Phys. 92679 (1970)
Exciting photons in a cavity with a moving mirror
c is the speed of light
Experimentally always in the adiabatic regime
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Splitting condensate on Y-junction beyond
mean-field
K Luttinger parameter v is the condensate
velocity
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Splitting with acceleration Unruh like effect
Fagnocchi, Altman, Demler
Splitting condensates with relativistic
acceleration gives rise to thermal
correlations. This is analogous to the Unruh
effect in field theory and quantum gravity Unruh
(1974), Fulling and Davies (1976)
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Summary
Interference experiments with ultracold atoms
provide a powerful tool for analyzing
equilibrium properties and dynamics of many-body
systems. Analysis beyond mean-field and single
mode approximation is needed important
Thanks to