Fermi Gases in Slowly Rotating Traps: Superfluid vs Collisional Hydrodynamics

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Fermi Gases in Slowly Rotating TrapsSuperfluid
vs Collisional Hydrodynamics

• Marco Cozzini and Sandro Stringari
• Università di Trento and BEC-INFM

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RECENT EXPERIMENTS WITH FERMI GASES NEAR A
FESHBACH RESONANCE HAVE REVEALED STRONG
INTERACTION EFFECTSHYDRODYNAMIC
EXPANSION(DUKE, JILA, ENS)FORMATION OF
MOLECULES (agt0)(JILA, ENS) both effects are
compatible with superfluidity but do not test it
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Hydrodynamics predicts anisotropic expansion in
Fermi superfluids (Menotti et al, PRL 89,
250402(2002))
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Anisotropic expansion in Fermi gases - test
of hydrodynamic forces- test of superfluidity
only if normal gas is collisionless and
expands ballistically (true at low T far from
Feshbach resonance)
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PLAUSIBLE SCENARIONear a Feshbach resonance a
Fermi gas exhibits universal hydrodynamic
behaviour

• Below Tc hydrodynamics is due to superfluidity
• Above Tc hydrodynamics is due to collisions

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Can we distinguish between superfluid and
collisional hydrodynamics?

• NO if we consider irrotational flow (for example
  expansion)
• YES if we look for vorticity effects

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POSSIBLE TEST OF SUPERFLUIDITY IN TRAPPED FERMI
GASES ROTATIONAL PROPERTIES (PROBE TRANSVERSE
RESPONSE)

• QUANTIZED VORTICES (cannot be described by
  hydrodynamics)
• MOMENT OF INERTIA (described by hydrodynamics)

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Outline

• Superfluid (irrotational) and Collisional
  (rotational) Hydrodynamics
• Collective Oscillations without rotation
• Collective oscillations with rotating trap test
  of superfluidity

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Hydrodynamic equations
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Recent applications of rotational hydrodynamics
to Bose-Einstein condensed gases containing many
vortical lines (diffused vorticity) M. Cozzini
and S. Stringari, Phys. Rev.A 67, 041602
(2003) F. Chevy and S. Stringari, Kelvin modes,
in preparation

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Hydrodynamic Equations)
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Collisional (rotational) hydrodynamics
zero-order approximation of Boltzmann equation
(no viscosity)
Superfluid (irrotational) hydrodynamics
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Expansion of non rotating gas - Collective
oscillations built on top of non rotating
gasSAME BEHAVIOUR IN SUPERFLUID AND COLLISIONAL
HYDRODYNAMICS(including scissors oscillation !!)
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Collective Oscillations (static trap)
Axisymmetric case
Quadrupole oscillations
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Equation of state
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Rotating Harmonic Potential
Stationary solutions in rotating frame
Rotational hydrodynamics
Time needed to spin up a normal gas by rotating
the trap Small static anisotropy unimportant
in hydrodynamic regime
Irrotational hydrodynamics
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TIME NEEDED TO SPIN UP A NORMAL GAS IN
HYDRODYNAMIC REGIME (Guery-Odelin, 2000)
Small static anisotropy unimportant in
hydrodynamic regime
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SPLITTING of m 2 and -2 QUADRUPOLE FREQUENCIES
(rotational hydrodynamics)twice the angular
velocity of the fluid
consistent with
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Rotational test of Superfluidity (1)

• Initial condition deformed trap rotating at
  small angular velocity
• Switch off trap deformation excitation of m2
  and m-2 quadrupole modes

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• Superfluid HD
• (b) collisional HD

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In ENS experiment (Chevy et al.,2000) b-0 and
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Rotational test of Superfluidity (2)

• Initial condition deformed trap rotating at
  small angular velocity
• Stop the rotation of the trap excitation of the
  scissors mode

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Collisional HD beating of m2 and m-2 modes
Superfluid HD oscillation with scissors frequency
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1. Superfluid HD
2. Collisional HD

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Conclusion

• Rotation of trapped Fermi gas at small angular
  velocity natural tool to test superfluidity