1. Pairing Gaps in the BEC-BCS crossover regime 15/06/2005, Strong correlations in Fermi systems Cheng Chin JFI and Physics, University of Chicago Exp.: Rudolf Grimm’s group, Innsbruck University, Austria BECBCS a=±  Top 10 Science Breakthroughs of 2004 Winner: Two Rovers on Mars Runner up: Indonesian “hobbit” Human cloning Condensation of Fermionic atoms … ”Breakthrough of the Year”, Science, Dec. 17, 2004

2. Content How do we distinguish two-body pairing and many- body pairing? Peculiar system 6 Li –Why do we have 300G Feshbach resonance? Pairing gap and collective modes in the crossover… –Breakdown of the smooth crossover? What is the experimental gap δ ? –BEC limit –BCS limit –In general

3. Phase diagram of a two-component Fermi gas Binding energy (E F ) Temp. (T F ) Thermal Fermi gas Thermal bosons Deg. Fermi gas Bose-Einstein condensation Cooper pairing   chemistry Superconductor AMO 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 300G wide Feshbach resonnace No interaction Tunable interaction

5. Feshbach resonance: tuning the scattering length atomic separation potential -  B Transition matrix Scattering length Nice picture, but also wrong! -- Fano profile 

6. 6 Li 2 molecular energy (ab channel) Bare state Δ~40,000 E F R 0 =30 a 0 Δ=detuning Γ=Feshbach coupling

7. The Mag net ic handle: Feshbach resonance Scattering between |1> and |2> BEC regimeBCS regime 834G a>0a<0 mol. state 300G wide Feshbach resonnace Tunable interaction Tunable and stable, (Petrov et al., 2004)

8. Innsbruck: 6 Li BEC-BCS crossover na 3 = 0.001k F a = - 0.5 a = ±  density profile Bartenstein et al., PRL 04 Radial Compression Mode Axial Breathing Mode 1/k F a Bartenstein et al., PRL 04 gap Chin et al., Science 04 δ

9. rf In the molecule picture Pairing gap measurement: RF excitation State 3 is initially unpopulated f atom = E 23 f molecule = E 23 +E b +2E K atomsmolecules EbEb Excitation rate

10. Pairing in the BEC regime T´ >> T F T´ ~ T F T´ < 0.2 T F RF offset (kHz) molecules only atoms only mixture EbEb excitation rate (a.u.) BEC limit 720G a=2180a 0 k F a=0.4 Also by JILA group Excellent agreement Experiment Bartenstein et al., PRL 05 Theory Chin and Julienne, PRA 05

11. Radio-frequency spectroscopy on molecules Bound-free transitions EXPERIMENT: Bound-free transitions 720.13(4)GRF:82.593(2)MHz 694.83(4)GRF:82.944(2)MHz Bound-bound transitions 676.09(3)GRF:83.2966(5)MHz 661.44(2)GRF:83.6645(3)MHz THEORY (Simoni, Tiesinga, Julienne) a s =45.167(8)a0, a T =-2140(18)a0 Feshbach resonance positions |1>+|2>: 834.1  1.5 G Resonance width: 300G  Exp: M. Bartenstein et al, PRL 94, 103201 Theo: C. Chin and P. Julienne, PRA 71, 012713

12. RF offset (kHz) RF offset (E F ) excitation rate (875 G ka=-3) T´ >> T F 0.5 T F < 0.2 T F Creation of a hole in state 2 and then a particle in state 3 with zero momentum transfer. Energy cost: 0.06 E F RF excitation (BCS regime)

13. Pairing gap vs. Temperature (psuedo gap?) 0.36 0.3 0.25 << 0.1 T/T F 0.38T F 0.26T F ~ T c 0.18T F 0.10T F T Theory C. Chin et al., Science 04 J. Kinnunen et al., Science 04 Calibrated by K. Levin Other theory: H. Heiselberg: supergap A. Griffin: Andreev states Yu and Baym: SU(2) symmetry breaking

14. Last evidence: Pairing gaps vs. Fermi energies Two-body calculation gap T F = 3  K dense clould T F = 1  K dilute cloud BEC regime BCS regime

15. RF pairing gap δ approaches E b in the BEC limit Δ 2 /E F in the BCS limit. Conjecture: δ= Conclusion and Future RF pairing gap δ vanish due to dimensionality? Others: A unified theory for RF with the right limit? Broadening of the narrow feature Pseudo gap Lack of mean-field shift??