1. Universal thermodynamics of a strongly interacting Fermi gas Hui Hu 1,2, Peter D. Drummond 2, and Xia-Ji Liu 2 1.Physics Department, Renmin University of China; 2.ACQAO, Physics Department, University of Queensland.

2. Why strongly interacting Fermi gases? Universal systems Lattice field theory Atomic Fermi gases with FR High Tc superconductors Quark-gluon plasma of Big Bang Neutron star matter Fermions are the building blocks of matter. Strongly-interacting Fermi gases are stable.

3. What is unitarity? L -V 0 R George Bertsch’s problem: from Thomas’ talk scattering l

4. B0B0 Magnetic-field Feshbach resonance: 6 Li and 40 K magnetic detuning 2 Unitarity: σ(k)=4π/k 2

5. Universality Conjecture: One length scale: L = n -1/3 Thermodynamics independent of structure

6. Universal thermodynamics in a harmonic trap

7. Experimental investigations of thermodynamics Optical Trap Loading Forced Evaporation High-Field Imaging Problem: no reliable thermometry !

8. Potential energy is obtained from axial cloud size mask Energy from interacting gas

9. B0B0 Isentropic sweep to the weak coupling BCS limit Isentropic Thermometry

10. Integrate x From Thomas- Fermi Fit: “true” temperature (entropy) for non-interacting gas mask Entropy from noninteracting gas

11. Nozieres and Schmitt-Rink theory

12. Mean field thermodynamic potential Where the free Nambu propagator:

13. Pair fluctuations Where the Cooper pair propagator:

14. Gap and particle number equations gap: i.e., num: i.e.,an additional term from conserving requirement

15. Other BCS-BEC crossover theories? TheoriesT amamamam Inter-molecule interactions (BEC) MFT=0 a m =2a F condensate-condensate Original NSRT>Tc a m =0a F None ! Strinati et al. (NSR)T=0 a m =2a F ??? HLDT=0 a m =0.57a F Includes pairing fluctuations “a m = 0.6a F ” within 2% accuracy, by Petrov et al., PRL, 2004

16. ? Comparison to the heat capacity data by Thomas et al. ( 6 Li) Cloud size at 840G gives Energy at unitarity (Virial theorem) Cloud size at 1200G gives Entropy at unitarity (isentropic sweep) The measurement of entropy is a conceptual advance owing to John Thomas et al., with accuracy at 1% level

17. Duke, Thomas group: L. Luo et al., PRL 98, 080402 (2007).

18. ? Comparison to the heat capacity data by Jin et al. ( 40 K) Cloud size at 202G gives potential energy at unitarity Noninteracting cloud size gives non-interacting temperature We then re-analyze the JILA data of potential energy and noninteracting temperature to obtain the energy and entropy.

19. JILA, Jin group: J. T. Stewart et al., PRL 97, 220406 (2006).

20. Evidence for Universality

21. Perturbation vs Monte Carlo Homogeneous Case Energy vs T Entropy vs T

22. Comparative Studies in a trap

23. What about many Fermi species? Color Superconductors! Exactly soluble problem in one-dimension - use LDA to treat a trap

24. Deconfining transition - evidence from breathing mode frequencies

25. BCS-BEC crossover with unequal spin populations !

26. Like a dance floor with more men than women, the state contains paired and unpaired entities

27. Expt.: M. W. Zwierlein et al. Science 311, 492 (2006). Expt.: G. B. Partidge et al. Science 311, 503 (2006). Quantum Phase Transition Experiments: Polarized Fermi gases Phase Separation

28. Questions What is the ground state of a polarized Fermi gas? What is the ground state of a polarized Fermi gas? Does the FFLO state exist? Does the FFLO state exist? What is the structure of FFLO state? What is the structure of FFLO state? What is the intrinsic reason for the phase separation state? What is the intrinsic reason for the phase separation state? Is there any uniform superfluid state with a finite spin population imbalance (i.e., p c ~ 0.10 in the unitary limit)? Is there any uniform superfluid state with a finite spin population imbalance (i.e., p c ~ 0.10 in the unitary limit)?  c = 0.74 in the unitary limit?  c = 0.74 in the unitary limit?

29. Polarized Fermi Gas in One Dimension Method Mean-field Exact solution SPWA SCBd G

30. Phase Diagram of a Uniform System Spin polarizationdimensionless parameter Integrable Gaudin Equations (Bethe Ansatz):

31. Phase Diagram of a Uniform System SF : BCS-like superfluid state with zero polarization SF P : Superfluid state with finite polarization N : Fully polarized normal state

32. Structure of SFp Phase P=0.0 3 P=0.16 The SFp is of FFLO Character

33. ?? PHASE DIAGRAM IN A ONE-DIMENSIONAL TRAP

34. Conclusions and references We analyze recent experimental measurements on the finite temperature properties of a strongly interacting atomic Fermi gas and provide evidence of universal thermodynamics. We analyze recent experimental measurements on the finite temperature properties of a strongly interacting atomic Fermi gas and provide evidence of universal thermodynamics. Extensions: exact solutions for: 1D color superconductors, polarized Fermi gasExtensions: exact solutions for: 1D color superconductors, polarized Fermi gas J. T. Stewart et al., Phys. Rev. Lett. 97, 220406 (2006). J. T. Stewart et al., Phys. Rev. Lett. 97, 220406 (2006). L. Luo et al., Phys. Rev. Lett. 98, 080402 (2007). L. Luo et al., Phys. Rev. Lett. 98, 080402 (2007). G. Partridge et al., Science 311, 503 (2006). G. Partridge et al., Science 311, 503 (2006). Hu, Liu & Drummond, Europhys. Lett. 74, 574 (2006). Hu, Liu & Drummond, Europhys. Lett. 74, 574 (2006). Hu, Liu & Drummond, Phys. Rev. A 73, 023617 (2006). Hu, Liu & Drummond, Phys. Rev. A 73, 023617 (2006). Hu, Drummond & Liu, 3 469, Nature Physics (2007). Hu, Drummond & Liu, 3 469, Nature Physics (2007).

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