1. University of Trento INFM

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

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

4. LINK BETWEEN BEC AND SUPERFLUIDITY PROVIDED BY ORDER PARAMETER  = n 1/2 e iS S = phase n = condensate density v = ( h / 2  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. HD equations hold in local density approximation (healing length << R; local description of chemical potential) Dilute BEC gas (a<<d) Dilute Fermi gas (a<<d)

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 Second pulse 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) BEC superfluid ideal gas collisional ideal gas collisionless m=0 radial m=0 axial m=2,-2 radial

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 below T c : the superfluid oscillates with frequency (  x 2 +  y 2 ) 1/2 Scissors mode above T c : the gas oscillates with frequencies |  x   y | 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 Vortex lattices at Mit, 2001

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

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 OSCILLATION Cataliotti 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. 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 IS HYDRODYNAMIC BEHAVIOUR SAFE CRITERIUM TO PROBE FERMI SUPERFLUIDITY ?

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

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

36. Irrotational hydrodynamics (superfluids) vs rotational hydrodynamics (normal fluids)

37. ROTATIONAL HYDRODYNAMICS HOLDS IF NORMAL GAS IS COLLISIONAL or SUPERFLUID 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 GAS ROTATE 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 MOMENTUM vs ANGULAR 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