1. Precision collective excitation measurements in the BEC-BCS crossover regime 15/06/2005, Strong correlations in Fermi systems A. Altmeyer 1, S. Riedl 12, C. Chin 13, J.-H. Denschalg 1, and R. Grimm 12 1 Institute for Experimental Physics, Innsbruck University, Innsbruck, Austria 2 Institute for Quantum Optics and Quantum Information, Innsbruck, Austria 3 James Franck institute and Department of physics, U. of Chicago, USA

2. Experiments on ultracold Fermi gases Hydrohynamic expansion (Duke, ENS...) Bose condensate of molecules (Innsbruck, JILA, MIT) Vortices in fermionic superfluid (MIT) Fermions in optical lattices (ETH, Florence) BEC-BCS crossover (Science 04)

3. Phase diagram of a balanced two-component Fermi gas Binding energy (E F ) Temp. (T F ) Thermal Fermi gas Thermal bosons Deg. Fermi gas Bose-Einstein condensation Cooper pairing   Superconductor High-Tc He-3 6 Li M. Holland

4. The Mag net ic handle: Feshbach resonance Scattering between |1> and |2> BEC regimeBCS regime 834G a>0a<0 mol. state Our Fermi energy: h 15 kHz No interaction Tunable interaction

5. 6 Li experiment (Innsbruck, Austria) 6 Li Gas in a harmonic trap Fermi temperature~ 1  K Atomic separation ~ 200nm Interaction range ~ 1 nm Particle number~ 10 5 Geometry: 3D harmonic trap 100  m 4  m

6. Bose-Einstein condensation of Li 2 Evaporative cooling 2.6 s3 s3.6 s4.0 s BEC fraction 0~ 15%~ 30%> 90% Gaussian density profile thermal cloud BEC 676G a Jochim et al., Science (2003), Bartenstein et al., PRL (2004) Thomas - Fermi

7. Explore the BEC-BCS crossover Molecular BEC na 3 = 0.001 BEC regime cloud size scattering length (10 3 a 0 )

8. Strongly interacting BEC Molecular BEC na 3 = 0.001 na 3 = 0.28 BEC regime cloud size scattering length (10 3 a 0 ) Calculation based on molecular mean field

9. Resonant gas Molecular BEC na 3 = 0.001 na 3 = 0.28 |a|   BCS regimeBEC regime cloud size scattering length (10 3 a 0 )

10. Strongly interacting Fermi gas Molecular BEC na 3 = 0.001 na 3 = 0.28k F |a| = 6 |a|   BCS regimeBEC regime cloud size scattering length (10 3 a 0 )

11. Weakly interacting Fermi gas! Molecular BEC Deg. Fermi gas na m 3 = 0.001 na m 3 = 0.28 k F |a| = 0.6 k F |a| = 6 |a|   BCS regimeBEC regime cloud size scattering length (10 3 a 0 ) Bartenstein et al., PRL (2004) μ~na μ~n 2/3

12. collective modes axial compression cigar-shaped trap 25:1 quadrupole radial

13. collective modes in the crossover Stringari, Europhys. Lett. 65, 749 (2004) Hu, Minguzzi, Liu, Tosi, PRL 93, 190403 (2004) Heiselberg, PRL 93, 040402 (2004) Combescot, Leyronas, Europhys. Lett. 68, 762 (2005) Manini, Salasnich, PRA 71, 033625 (2005) Bulgac, Bertsch, PRL 94, 070401 (2005) Kim, Zubarev, PRA 72, 011603(R) (2005) Astrakharchik, Combescot, Leyronas, Stringari, PRL 95, 030404 (2005) … theory experiments: Duke; Innsbruck

14. µ  n  equation of state radial compression mode polytropic index → many-body physics !! is the system hydrodynamic ? no: yes: (collisionless Fermi gas) (superfluid or class. hydrodyn. gas) radial trap frequency osc. frequency BEC: µ  n unitarity: µ  n 2/3

15. radial compression mode (2004 data) frequency (normalized to sloshing mode) damping hydrodynamic collisionless Bartenstein et al., PRL 92, 203201 (2004)

16. radial compression mode (2004 data) frequency (normalized to sloshing mode) damping superfluid !!! collisionless Bartenstein et al., PRL 92, 203201 (2004) pair breaking ! uncontrolled trap ellipticity (~15%): quantitative deviations Ω x /ω x

17. radial compression mode exp. data from John Thomas group at Duke Kinast et al, PRA 70, 051401 (2004) theory: mean field BCS à la Leggett, Nozières & Schmitt-Rink Hu et al., PRL 93, 190403 (2004) BEC BCS expt. data consistent with mean-field BCS theory! ?

18. beyond mean field Phys. Rev. 105, 1119 (1957) leading correction is positive → upshift of collective-mode frequency in mBEC regime ! Lee-Huang-Yang correction

19. quantum Monte Carlo Lee-Huang-Yang correction !!! Lee-Huang-Yang correction !!! BEC BCS

20. radial mode exp. data from John Thomas group at Duke Kinast et al, PRA 70, 051401 (2004) theory: mean field BCS à la Leggett, Nozières & Schmitt-Rink Hu et al., PRL 93, 190403 (2004) BEC BCS quantum Monte Carlo, Astrakharchik et al., PRL 95, 030404 (2005) see also Manini and Salasnich, PRA 71, 033625 (2005) ?

21. Experiment improvement Ellipticity of the trapping beam New imaging system Lower temperatures? 6 Li

22. 764G: na m 3 ~0.01 Experiment improvement Confirm J. Thomas group observation Lowest damping Γ/ω < 0.01

23. precision measurements sloshing modes beat reveals trap ellipticity of ~6% horizontal vertical can be measured with ~10 -3 uncertainty anharmonicity effects in Gaussian trap potential ~2% suppressed to few 10 -3 by normalization to sloshing mode compression mode accurate determination of frequency needs very low damping  optimized cooling !

24. radial mode (new data) BEC BCS

25. new measurements on collective modes confirm equation of state from quantum Monte-Carlo calculations and LHY correction rule out simple mean-field BCS theory for crossover new measurements on collective modes confirm equation of state from quantum Monte-Carlo calculations and LHY correction rule out simple mean-field BCS theory for crossover precision test of many-body theories ! Beyound L-Y correction?