Ultracold Fermi gases

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 • - spinpolarizability 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 (O’Hara et al, 2003) normal collisionless

6. Pair correlations of an expanding superfluid Fermi gasC. 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 HDapproximation • (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

12. COLLECTIVE OSCILLATIONS AND EQUATION OF STATE

13. COLLECTIVE OSCILLATIONS IN SUPERFLUID PHASE (T=0) • - Surface modes: unaffected by equation of state • - Compression modes sensitive to equation of state. • Theory of superfluids predicts • universal values when 1/a=0 : • - 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

26. SF 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