Diapositiva 1

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BEC Meeting, Trento, 2-3 May 2006
Ultracold Fermi gases
Sandro Stringari
University of Trento
INFM-CNR
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Atomic Fermi gases in traps
Ideal realization of non-interacting
configuarations with
spin-polarized samples - Bloch oscillations and
sensors (Carusotto et al.), - Quantum
register (Viverit et al) - Insulating-conducting
crossover (Pezze et al.)

• Role of interactions (superfluidity)
• HD expansion (aspect ratio and pair correlation
  function)
• collective oscillations and equation of state
• - spin polarizability

This talk
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EXPANSION OF FERMI SUPERFLUID
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Hydrodynamics predicts anisotropic expansion of
BEC gas
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Hydrodynamics predicts anisotropic expansion in
Fermi superfluids (Menotti et al,2002)
HD theory
Evidence for hydrodynamic anisotropic expansion
in ultra cold Fermi gas (OHara et al, 2003)
normal collisionless
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Pair correlations of an expanding superfluid
Fermi gas C. Lobo, I. Carusotto, S. Giorgini, A.
Recati, S. Stringari, cond-mat/0604282
Recent experiments on Hanbury-Brown Twiss effect
with thermal bosons (Aspect, Esslinger, 2005)
provide information on

• Pair correlation function measured after
  expansion
• Time dependence calculated in free expansion
  approximation
• (no collisions)
• Decays from 2 to uncorrelated value 1
• (enhancement at short distances due Bose
  statistics).
• For large times decay lengths approach
• anisotropic law

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QUESTION
Can we describe behaviour of pair correlation
function during the expansion in strongly
interacting Fermi gases (eg. at unitarity) ?

• In situ correlation function calculated with MC
  approach
• (see Giorgini)
• Time dependence described working in HD
  approximation
• (local equilibrium assumption)

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unitarity
BEC limit
thermal bosons
Pair spin up-down correlation function
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• Pair correlation function in interacting Fermi
  gas
• Spin up-down correlation function strongly
  affected by
• interactions at short distances.
• Effect is much larger than for thermal bosons
• (Hanbury-Brown Twiss)
• In BEC regime ( ) pair correlation
  function approaches
• uncorrelated value 1 at distances of the order
  of
• scattering length (size of molecule)
• At unitarity pair correlation function
  approaches value 1
• at distances of the order of interparticle
  distance
• (no other length scales available at unitarity)

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Local equilibrium ansatz for expansion

• Dependence on s fixed by equilibrium result
• (calculated with local value of density)
• - Time dependence of density determined by HD
  equations.

• Important consequences
• (cfr results for free expansion of thermal
  bosons)
• Pair correlation keeps isotropy during
  expansion
• Measurement after expansion measures
  equilibrium
• correlation function at local density
• at unitarity, where correlation function depends
  on
• combination , expansion acts like a
  microscope

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COLLECTIVE OSCILLATIONS AND EQUATION OF STATE
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COLLECTIVE OSCILLATIONS IN SUPERFLUID PHASE (T0)

• - Surface modes unaffected by equation of state
• - Compression modes sensitive to equation of
  state.
• Theory of superfluids predicts
• universal values when 1/a0
• - In BEC regime one insetad finds

Behaviour of equation of state through the
crossover can be inferred through the study of
collective frequencies !
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Radial compression mode
S. Stringari, Europhys. Lett. 65, 749 (2004)
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• Experiments on collective oscillations at
• - Duke (Thomas et al..)
• - Innsbruck (Grimm et al.)

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Duke data agree with value 1.826 predicted at
unitarity
(mean field BCS gap eq.)
unitarity
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Radial breathing mode at Innsbruck (2006)
(unpublished)
MC equation of state
BCS mean field
Theory from Astrakharchik et al Phys. Rev. Lett.
95, 030405 (2005)
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Crucial role of temperature - Beyond mean field
(LHY) effects are easily washed out by thermal
fluctuations finite T (Giorgini 2000) Conditions
of Duke experiement - Only lowering the
temperature (new Innsbruck exp) one can see LHY
effect
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SPIN POLARIZABILITY
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Spin Polarizability of a trapped superfluid Fermi
gasA. Recati, I. Carusotto, C. Lobo and S.S.,
in preparation
Recent experiments and theoretical studies have
focused on the consequence of spin polarization
( ) on the
superfluid features of interacting Fermi gases
MIT, 2005
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In situ density profiles for imbalanced
configurations at unitarity (Rice, 2005)
Spin-up
Spin-down
difference
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An effective magnetic field can be produced by
separating rigidly the trapping potentials
confining the two spin species.
For non interacting gas, equilibrium corresponds
to rigid displacement of two spin clouds in
opposite direction
This yields spin dipole moment (we assume
)
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We propose a complementary approach where we
study the consequence of an effective magnetic
field which can be tuned by properly modifying
the trapping potentials.
Main motivation Fermi superfluids cannot be
polarized by external magnetic field unless it
overcomes a critical value (needed to break
pairs).
What happens in a trapped configuration? What
happens at unitarity ?
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In the superfluid phase atoms like to be paired.
and feel the x-symmetric potential
Competition between pairing effects and external
potential favouring spin polarization
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At unitarity
Equilibrium between superfluid and spin polarized
phases (Chevy 2005)
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Spin dipole moment D(d)/d as a function of
separation distance d (in units of radius of the
cloud)
ideal gas
Deep BEC
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Further projects - Collective oscillations of
spin polarized superfluid - Rotational effects in
spin polarized superfluids