Ultracold Fermi gas near Feshbach resonance with mass

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

Outline u BEC, Superfluidity u BEC-BCS crossover u Polarized Fermi gas with mass imbalance u Prospective work

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)

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

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

Feshbach resonance Closed 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)

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)

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

Population imbalance: FFLO states FFP. Fulde and R. A. Ferrel PR 135, A 550 (1964) LOA. 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)

Polarized Fermi gas with mass mismatch u Hamiltonian u Order parameter, Gap h

Polarized Fermi gas with mass mismatch u Center-of-mass frame Reduced mass Interaction rate

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

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

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

Phase boundaries under various detuning for 6 Li-40 K ( =0. 74) (k. Fas)-1=-1 (k. Fas)-1=0 BCS SF: superfluid Resonance p NM: normal mixture (2 species) NP: normal polarized phase (1 species) p (k. Fas)-1=0. 2 (k. Fas)-1=0. 5 BEC r/R

Density profiles and Shell structure On resonance (k. Fas)-1=0 T/TF=0 p=0. 2 Li K=Li T/TF=0. 1 K>Li Superfluid

Density profiles and Shell structure (k. Fas )-1= -1 BCS Li Li>K K=Li K>Li p = -0. 4 (k. Fas )-1= 0. 2 BEC Superfluid K=Li p = 0. 3 K>Li (T= 0)

Quasiparticle energy spectrum Superfluid $ nontrivial • Ek Equal population, no mass mismatch: h=0, =0 0 • Imbalanced case: h 0, 0, in general. k For 0 Ek Regular SF Ek BP 1 Ek BP 2 k k k

Thermodynamical potential: Double- and single-well transition = ( (r), h) for 6 Li-40 K, p=0. 2 (T=0, resonance) ~

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

Perspective work u FFLO states u Finite T u Finite size effect u Vortices