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Bulletin of the American Physical Society

Effect of Zeeman Field and Spin-Orbit Coupling on Fermi Gases in Optical Lattices

Haiyang Zhang, Hai‐Chao Li, X Xiong, Guo-Qin Ge

Published Mar 14, 2017• 0 citations
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arXiv:1304.3926•Physical Review A•May 16, 2014•21 citations
We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to (i) Fulde-Ferrell-like superfluidity and (ii) skyrmionlike polarization textures near the edges of the system. We also discuss the effects of interaction, temperature, SOC anisotropy, and Zeeman field anisotropy on the superfluid ground-state and polarization textures.
We investigate the single-particle and collective excitations of a Rashba spin-orbit-coupled atomic Fermi gas with attractive interaction, loaded in a two-dimensional (2D) square optical lattice, in the presence of an effective out-of-plane Zeeman field. Our numerical calculations show that the many-body physics of the Bardeen-Cooper-Schrieffer (BCS) side is strongly modified compared to the Fermi gases in the free space. The physics behind this statement lies in the fact that in the 2D lattice case the single-particle ground-state energy is four times degenerated, while without a lattice structure the ground state is infinitely degenerate, and because of that, the spin-orbit coupling (SOC) in optical lattices gives rise to unusual properties entirely different from the continuum. For example, in the continuum, the pairing gap as well as the condensate fraction is strongly enhanced by the SOC strength on the BCS side. In the presence of lattice geometry the gap and the condensate fraction increase as a function of the SOC strength only at small fillings and a weak attraction limit. Moreover, we found that the speed of sound also exhibits different behavior: in the 3D and 2D continua, the slope of the Goldstone mode decreases as a function of the SOC strength, while in the lattice case the speed of sound increases monotonically with the SOC strength.
The recent experimental realization of spin-orbit (SO) coupling for ultracold atoms opens a completely new avenue for exploring new quantum matters. In experiments, the SO coupling is implemented simultaneously with a Zeeman field. Such SO-coupled Fermi gases are predicted to support Majorana fermions with non-Abelian exchange statistics in one dimension (1D). However, as shown in recent theory and experiments for 1D spin-imbalanced Fermi gases, the Zeeman field can lead to the long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids with nonzero center-of-mass momentum Cooper pairings, in contrast to the zero center-of-mass momentum pairings in Majorana superfluids. Therefore a natural question to ask is which phase, FFLO or Majorana superfluids, will survive in SO-coupled Fermi gases in the presence of a large out-of-plane Zeeman field. In this paper, we address this question by studying the mean-field quantum phases of 1D (quasi-1D) SO-coupled fermionic cold-atom optical lattices.