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University of Trento

INFM. University of Trento. BOSE-EINSTEIN CONDENSATION IN TRENTO. University of Trento. SUPERFLUIDITY IN TRAPPED GASES. Inauguration meeting, Trento 14-15 March 2003. BOSE-EINSTEIN CONDENSATION vs SUPERFLUIDITY. OLD PUZZLE IN CONDENSED MATTER PHYSICS. LINK BETWEEN

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University of Trento

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  1. INFM University of Trento

  2. BOSE-EINSTEIN CONDENSATION IN TRENTO University of Trento SUPERFLUIDITY IN TRAPPED GASES Inauguration meeting, Trento 14-15 March 2003

  3. BOSE-EINSTEIN CONDENSATIONvs SUPERFLUIDITY OLD PUZZLE IN CONDENSED MATTER PHYSICS

  4. LINK BETWEEN BEC ANDSUPERFLUIDITY PROVIDED BY ORDER PARAMETER  =n1/2 eiS S =phase n =condensate density v = ( h / 2p m)  S=superfluid velocity (IRROTATIONALITY ! )

  5. SUPERFLUIDITY IN TRAPPED GASES • Dynamics (sound, oscillations, expansion) • Rotational effects (scissors and vortices) • Josephson effect • Fermi gases

  6. IRROTATIONAL HYDRODYNAMICS(Bose and Fermi superfluids)

  7. Dilute BEC gas (a<<d) Dilute Fermi gas (a<<d) HD equations hold in local density approximation (healing length << R; local description of chemical potential)

  8. PREDICTIONS OF IRROTATIONAL HYDRODYNAMICS • BOGOLIUBOV SOUND • COLLECTIVE OSCILLATIONS • ANISOTROPIC EXPANSION

  9. Sound in a Bose gas Mit, 97

  10. Measurement of Bogoliubov amplitudes Theory ( double Bragg pulse) First pulse generates phonons Secondpulse measures their momentum distribution Brunello et al. PRL85, 4422(2000) Exp: Vogels et al. PRL88, 060402 (2002)

  11. Collective oscillations in hydrodynamic regime (cigar trap)

  12. Collective oscillations, T=0 BEC, Mit 97 exp: theory (HD):

  13. Hydrodynamics predicts anisotropic expansion of the condensate

  14. SUPERFLUIDITY IN TRAPPED GASES • Dynamics (sound, oscillations, expansion) • Rotational effects (scissors and vortices) • Josephson effect • Fermi gases

  15. Scissors mode

  16. Scissors mode belowTc: the superfluid oscillates with frequency ( wx2 + wy2 )1/2 Scissors mode aboveTc: the gas oscillates with frequencies | wxwy | Guery-Odelin and Stringari, PRL 83, 4452 (1999)

  17. Scissors at Oxford Marago’et al, PRL 84, 2056 (2000) above Tc below Tc

  18. QUANTIZED VORTICES ( r ,  ) =  ( r) e i • Circulation of velocity is quantized. Quantum of circulation: h/m • First obtained at Jila (phase imprinting) • Realized at ENS by rotating the trap at “high”angular velocity • Nucleation of vortices associated with instabilities against surface deformation

  19. Quantized vortices at ENS (2001) F. Chevy et al.

  20. Vortex lattices at Mit, 2001 Vortex lattices

  21. Measurement of angular momentum • SPLITTING between m=+2 and m=-2 quadrupole frequencies (Zambelli and Stringari, 1998) • PRECESSION

  22. Shape precession in the presence of a quantized vortex (Jila 2001)

  23. Measurement of angular momentum in BEC gas (Chevy et al., PRL 85, 2223 (2000))

  24. SUPERFLUIDITY IN TRAPPED GASES • Dynamics (sound, oscillations, expansion) • Rotational effects (scissors and vortices) • Josephson effect • Fermi gases

  25. JOSEPHSON OSCILLATIONS • CONDENSATE TRAPPED IN OPTICAL LATTICE +HARMONIC TRAPPING • CONDENSATE CAN COHERENTLY TUNNEL THROUGH THE BARRIERS

  26. DIPOLE OSCILLATIONCataliotti et al, Science 293, 843 (2001) tunneling rate distance between wells

  27. Josephson oscillation in optical trap Cataliotti et al. Science 293, 843 (2001)

  28. SUPERFLUIDITY IN TRAPPED GASES • Dynamics (sound, oscillations, expansion) • Rotational effects (scissors and vortices) • Josephson effect • Fermi gases

  29. RECENT WORK ON RESONANCE SUPERFLUIDITY(Holland, Griffin, Timmermans, Stoof, Combescot) • Availability of Feshbach resonances permits to reach favourable conditions for superfluidity • BCS-BEC crossover (Randeria, 1993)

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

  31. Evidence for hydrodynamic anisotropic expansion in a cold Fermi gas (O’Hara et al, Science, Dec. 2003)

  32. O’Hara et al, Science, Dec 2003

  33. IS HYDRODYNAMIC BEHAVIOUR SAFE CRITERIUM TO PROBE FERMI SUPERFLUIDITY ? • IN THE PRESENCE OF FESHBACH RESONANCE MEAN FREE PATH CAN BECOME SMALLER THAN SIZE OF THE SYSTEM GIVING RISE TO COLLISIONAL REGIME EVEN IN NORMAL PHASE

  34. akF=1 JILA (Regal and Jin, Feb 2003)

  35. HOW TO DISTINGUISH BETWEEN SUPERFLUID AND COLLISIONAL HYDRODYNAMICSLOOK AT ROTATIONAL EFFECTS

  36. Irrotational hydrodynamics (superfluids)vsrotational hydrodynamics(normal fluids)

  37. ROTATIONAL HYDRODYNAMICS HOLDS IFNORMAL GAS IS COLLISIONALorSUPERFLUID HAS MANY VORTICES (diffused vorticity), Cozzini and Stringari, PRA in press

  38. SPLITTING OF QUADRUPOLE FREQUENCIES PREDICTED BY ROTATIONAL HYDRODYNAMICS: consistent with rigid value estimate of angular momentum in

  39. SPLITTING OF QUADRUPOLE FREQUENCIES IN BEC GAS WITH MANY VORTICES (JILA, 2001)

  40. HOW TO PROBE SUPERFLUIDITY IN A COLD FERMI GASROTATE A SLIGHTLY DEFORMED TRAP AT SMALL ANGULAR VELOCITY (NO VORTICES) • SUPERFLUID. No angular momentum. No quadrupole frequency splitting • NON SUPERFLUID. Collisions thermalize the system to rigid rotation. Quadrupole frequencies are splitted.

  41. ANGULAR MOMENTUMvsANGULAR VELOCITY

  42. OTHER TOPICS RELATED TO SUPERFLUIDITY • Critical velocity and critical angular velocity • Systems of reduced dimensionality • Phase transition to Mott insulator phase • Superfluidity vs. disorder

  43. MAIN CONCLUSION • TRAPPED ATOMIC GASES: WELL SUITED TO EXPLORE THE EFFECTS OF SUPERFLUIDITY • MORE IN NEXT TALKS

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