Interference between independent cold atom systems

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Interference between independent cold atom
systems
Anatoli Polkovnikov, Boston University
Collaboration
Ehud Altman - The Weizmann Institute of
Science Eugene Demler - Harvard
University Vladimir Gritsev - Harvard
University
Workshop on Quantum Noise in Strongly Correlated
Systems. Weizmann Institute, Jan. 2008
AFOSR
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Interference between independent
sources. (Hanbury-Brown Twiss effect)
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Interference between independent
sources. (Hanbury-Brown Twiss effect)
Origin of interference superposition principle.
Intensity-intensity correlator survives!
HBT effect is the classical wave phenomenon!
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From classical waves to quantum particles
Origin of interference superposition principle.
Interference term drops out for uncorrelated
sources
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Interference between two condensates.

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What do we observe?
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(No Transcript)
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Define an observable (interference amplitude
squared )
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Interference from multiple sources
Having many particles in each condensate does not
reduce noise in the interference amplitude.
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Extended Condensates.
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Scaling with L two limiting cases
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Formal derivation
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Intermediate case (quasi long-range order).
1D condensates (Luttinger liquids)
z
Repulsive bosons with short range interactions
Finite temperature
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Observing the Kosterlitz-Thouless transition
Above KT transition
Lx??Ly
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Higher Moments (More in talk by V. Gritsev)
is an observable quantum operator
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Two simple limits
Strongly interacting Tonks-Girardeau regime
Central limit theorem! Also at finite T.
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Connection to the impurity in a Luttinger liquid
problem.
(more in V. Gritsev talk on Thursday).
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Evolution of the distribution function.
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Universal Gumbel distribution at large K
(?-1)/??
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Generalized extreme value distribution
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Detecting fermionic superfluidity (D-wave)
TOF
d
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Can go to 4th order correlation functions. Shot
noise will kill us.
Two ways around
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Fermions on a lattice.
Different orientations of imaging beams give
strong angular dependence of the signal in D-wave
case.
Can detect even the sign of the pairing gap using
two different imaging beams for BL and BR and
having one D-condensate and one S-condensate.
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Conclusions.
Two sources of noise in the interference a)
thermal or quantum fluctuationsb) shot
noise Mean amplitude of interference contains
information on two-particle correlation
functions. Higher moments contain additional
information. Interference is a powerful tool for
studying correlated cold atom systems.