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Universal thermodynamics of a strongly interacting Fermi gas

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

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Universal thermodynamics of a strongly interacting Fermi gas

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  1. Universal thermodynamicsof a strongly interacting Fermi gas Hui Hu1,2, Peter D. Drummond2, and Xia-Ji Liu2 • Physics Department, Renmin University of China; • ACQAO, Physics Department, University of Queensland.

  2. Why strongly interacting Fermi gases? • Fermions are the building blocks of matter. • Strongly-interacting Fermi gases are stable.

  3. George Bertsch’s problem: R -V0 L What is unitarity? scattering l from Thomas’ talk

  4. magnetic detuning Unitarity: σ(k)=4π/k2 B0 Magnetic-field Feshbach resonance: 6Li and 40K

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

  6. Universal thermodynamics in a harmonic trap

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

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

  9. Isentropic Thermometry B0 Isentropic sweep to the weak coupling BCS limit

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

  11. Nozieres and Schmitt-Rink theory

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

  13. Where the Cooper pair propagator: Pair fluctuations

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

  15. Other BCS-BEC crossover theories? “am = 0.6aF”within 2% accuracy, by Petrov et al., PRL, 2004

  16. Comparison to the heat capacity data by Thomas et al. (6Li) ? • 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. (40K) ? • 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. Experiments: Polarized Fermi gases Quantum Phase Transition Phase Separation Expt.:M. W. Zwierlein et al. Science311, 492 (2006). Expt.:G. B. Partidge et al. Science311, 503 (2006).

  28. Questions • What is the ground state of a polarized Fermi gas? • Does the FFLO state exist? • What is the structure of FFLO 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., pc~ 0.10 in the unitary limit)? • c = 0.74 in the unitary limit?

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

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

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

  32. Structure of SFp Phase P=0.03 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. • Extensions: exact solutions for: 1D color superconductors, polarized Fermi gas • J. T. Stewart et al., Phys. Rev. Lett.97, 220406 (2006). • L. Luo et al., Phys. Rev. Lett. 98, 080402(2007). • G. Partridge et al., Science311, 503 (2006). • Hu, Liu & Drummond, Europhys. Lett. 74, 574 (2006). • Hu, Liu & Drummond, Phys. Rev. A73, 023617 (2006). • Hu, Drummond & Liu, 3 469, Nature Physics (2007).

  35. NEW OPPORTUNITIES:PHD SCHOLARSHIPS AND POSTDOCSTHEORY AND EXPERIMENTSWINBURNE UNIVERSITYMELBOURNEAUSTRALIA

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