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Ultracold Fermi gas near Feshbach resonance with mass and population imbalance

Ultracold Fermi gas near Feshbach resonance with mass and population imbalance. Advisor: Prof. Luming Duan Committee: Prof. Luming Duan Prof. Georg Raithel Prof. Samuel Moukouri. Guin-Dar Lin Department of Physics University of Michigan August 25, 2006. Outline. BEC, Superfluidity

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Ultracold Fermi gas near Feshbach resonance with mass and population imbalance

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  1. Ultracold Fermi gas near Feshbach resonance with mass and population imbalance Advisor: Prof. Luming Duan Committee: Prof. Luming Duan Prof. Georg Raithel Prof. Samuel Moukouri Guin-Dar Lin Department of Physics University of Michigan August 25, 2006

  2. Outline • BEC, Superfluidity • BEC-BCS crossover • Polarized Fermi gas • Polarized Fermi gas with mass imbalance • Prospective work

  3. Bose-Einstein Condensate E. Cornell, J.Res.Natl.Inst.Stand.Technol., 101, 419 (1996) -Special state of matter in which macroscopic numbers of atoms occupy the same quantum state. W.Ketterle, Rev.Mod.Phys.74,1131 (2002)

  4. BEC of Fermionic pairs 40K condensate C.A.Regal, M.Greiner, and D.S.Jin PRL.92, 040403 (2004) 6Li condensate M.W. Zwierlein, C.A. Stan, C.H. Schunck, S.M.F. Raupach, A.J. Kerman, and W. Ketterle PRL.92,120403 (2004)

  5. Superfluidity in Fermi condensate M.W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, and W. Ketterle Nature 435 , 1047-1051 (2005)

  6. Feshbach resonanceClosed and open channels closed open S. Inouye and et al., Nature 392, 151 (1998) Left Figure from Q. Chen and et al., Physics Reports 412, 1-88 (2005) Right Figure from R.A. Duine and H.T.C. Stoof, Physics Reports, 396, 115 (2004)

  7. BEC-BCS crossover Tables from http://cua.mit.edu/ketterle_group/experimental_setup/BEC_I/Q_and_A.htm#rotation Figures from Q. Chen and et al. Physics Reports 412, 1-88 (2005)

  8. Polarized Fermi gas M.W. Zwierlein, A. Schirotzek, C.H. Schunck, and W. Ketterle Science 311, 492 (2006)

  9. Population imbalance: FFLO states FF- P. Fulde and R.A. Ferrel PR 135, A550 (1964) LO- A.I. Larkin and Y.N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1965) FFLO state: Finite-momentum pairing Q D.E. Sheehy and L. Radzihovsky PRL 96, 060401 (2005)

  10. h Polarized Fermi gas with mass mismatch • Hamiltonian • Order parameter, Gap

  11. Polarized Fermi gas with mass mismatch • Center-of-mass frame Reduced mass Interaction rate

  12. Polarized Fermi gas with mass mismatch • Thermodynamical Potential Mass mismatch parameter: Quasiparticle energy: Local Density Approximation:

  13. Polarized Fermi gas with mass mismatch • Number equations r 0 In the following discussion, heavy atom is taken for spin up, and light atom is taken for spin down, so that  > 0 always holds.

  14. System Characteristics Energy scale: Length scale: Wave number scale: Number density scale: Temperature scale: mass mismatch normalized temperature polarization detuning

  15. Phase boundaries under various detuning for 6Li-40K (=0.74) (kFas)-1=-1 (kFas)-1=0 BCS Resonance p SF: superfluid NM: normal mixture (2-species) NP: normal polarized phase (1-species) p (kFas)-1=0.2 (kFas)-1=0.5 BEC BEC r/R r/R

  16. p=0.2 Density profiles and Shell structure On resonance (kFas)-1=0 T/TF=0 Li T/TF=0.1 K=Li K>Li Superfluid

  17. Li Li>K K=Li K>Li p = -0.4 K=Li K>Li p = 0.3 Density profiles and Shell structure (kFas)-1= -1 BCS Superfluid (kFas)-1= 0.2 BEC (T= 0)

  18. Ek k Quasiparticle energy spectrum Superfluid $ nontrivial  Ek • Equal population, no mass mismatch: h=0, =0 • Imbalanced case: h 0,  0, in general.  0 k For  0 Ek Ek Regular SF BP1 BP2 k k

  19. ~ Thermodynamical potential:Double- and single-well transition  =  ((r),h) for 6Li-40K, p=0.2 (T=0, resonance)

  20. (I) (II) Fermi surfaces mismatch Formation of Superfluid: Local Fermi surfaces in k-space match

  21. Perspective work • FFLO states • Finite T • Finite size effect • Vortices

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