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Fermi Gases in Slowly Rotating Traps: Superfluid vs Collisional Hydrodynamics

Fermi Gases in Slowly Rotating Traps: Superfluid vs Collisional Hydrodynamics. Marco Cozzini and Sandro Stringari Università di Trento and BEC-INFM.

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Fermi Gases in Slowly Rotating Traps: Superfluid vs Collisional Hydrodynamics

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  1. Fermi Gases in Slowly Rotating Traps:Superfluid vs Collisional Hydrodynamics Marco Cozzini and Sandro Stringari Università di Trento and BEC-INFM

  2. RECENT EXPERIMENTS WITH FERMI GASES NEAR A FESHBACH RESONANCE HAVE REVEALED STRONG INTERACTION EFFECTS:HYDRODYNAMIC EXPANSION(DUKE, JILA, ENS)FORMATION OF MOLECULES (a>0)(JILA, ENS)both effects are compatible with superfluidity but do not test it

  3. Hydrodynamics predicts anisotropic expansion in Fermi superfluids(Menotti et al, PRL 89, 250402(2002))

  4. Anisotropic expansion in Fermi gases:- test of hydrodynamic forces- test of superfluidityonly if normal gas is collisionless and expands ballistically (true at low T far from Feshbach resonance)

  5. PLAUSIBLE SCENARIO:Near a Feshbach resonance a Fermi gas exhibits universal hydrodynamic behaviour • Below Tc hydrodynamics is due to superfluidity • Above Tc hydrodynamics is due to collisions

  6. Can we distinguish between superfluid and collisional hydrodynamics? • NO if we consider irrotational flow (for example: expansion) • YES if we look for vorticity effects

  7. 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)

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

  9. Hydrodynamic equations

  10. 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

  11. Hydrodynamic Equations)

  12. Collisional (rotational) hydrodynamics zero-order approximation of Boltzmann equation (no viscosity) Superfluid (irrotational) hydrodynamics

  13. Expansion of non rotating gas - Collective oscillations built on top of non rotating gasSAME BEHAVIOUR IN SUPERFLUID AND COLLISIONAL HYDRODYNAMICS(including scissors oscillation !!)

  14. Collective Oscillations (static trap) Axisymmetric case Quadrupole oscillations

  15. Equation of state

  16. RotatingHarmonic 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

  17. TIME NEEDED TO SPIN UP A NORMAL GAS IN HYDRODYNAMIC REGIME(Guery-Odelin, 2000) Small static anisotropy unimportant in hydrodynamic regime

  18. SPLITTING of m= 2 and -2 QUADRUPOLE FREQUENCIES (rotational hydrodynamics):twice the angular velocity of the fluid consistent with

  19. Rotationaltest of Superfluidity(1) • Initial condition: deformed trap rotating at small angular velocity • Switch off trap deformation: excitation of m=+2 and m=-2 quadrupole modes

  20. Superfluid HD • (b) collisional HD

  21. In ENS experiment (Chevy et al.,2000) b-=0 and

  22. Rotationaltest of Superfluidity(2) • Initial condition: deformed trap rotating at small angular velocity • Stop the rotation of the trap: excitation of the scissors mode

  23. Collisional HD: beating of m=+2 and m=-2 modes Superfluid HD: oscillation with scissors frequency

  24. Superfluid HD; • Collisional HD

  25. Conclusion • Rotation of trapped Fermi gas at small angular velocity: natural tool to test superfluidity

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