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Diapositiva 1

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Title: Diapositiva 1


1
BEC Meeting, Trento, 2-3 May 2006
Ultracold Fermi gases
Sandro Stringari
University of Trento
INFM-CNR
2
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
3
EXPANSION OF FERMI SUPERFLUID
4
Hydrodynamics predicts anisotropic expansion of
BEC gas
5
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
6
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

7
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)

8
unitarity
BEC limit
thermal bosons
Pair spin up-down correlation function
9
  • 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)

10
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

11
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12
COLLECTIVE OSCILLATIONS AND EQUATION OF STATE
13
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 !
14
Radial compression mode
S. Stringari, Europhys. Lett. 65, 749 (2004)
15
  • Experiments on collective oscillations at
  • - Duke (Thomas et al..)
  • - Innsbruck (Grimm et al.)

16
Duke data agree with value 1.826 predicted at
unitarity
(mean field BCS gap eq.)
unitarity
17
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)
18
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
19
SPIN POLARIZABILITY
20
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
21
In situ density profiles for imbalanced
configurations at unitarity (Rice, 2005)
Spin-up
Spin-down
difference
22
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
)
23
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 ?
24
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
25
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26
At unitarity
Equilibrium between superfluid and spin polarized
phases (Chevy 2005)
27
Spin dipole moment D(d)/d as a function of
separation distance d (in units of radius of the
cloud)
ideal gas
Deep BEC
28
Further projects - Collective oscillations of
spin polarized superfluid - Rotational effects in
spin polarized superfluids
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