Spin-orbit-coupled atomic Fermi gases in two-dimensional optical lattices in the presence of a Zeeman field

TL;DR

This paper explores how spin-orbit coupling and Zeeman fields influence the properties of a 2D lattice Fermi gas, revealing unique modifications in pairing, condensate fraction, and collective excitations compared to free space.

Contribution

It provides a detailed numerical analysis of the effects of lattice structure and spin-orbit coupling on the many-body physics of Fermi gases under Zeeman fields, highlighting differences from continuum systems.

Findings

Lattice structure reduces degeneracy of single-particle ground states compared to continuum.

SOC enhances pairing gap and condensate fraction only at small fillings and weak attraction.

Speed of sound increases monotonically with SOC strength in lattice systems, unlike in continuum.

Abstract

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 is in the fact that without a lattice structure, if the value of the Zeeman field does not exceed some threshold value, the minimum of the single-particle ground state energy is infinitely degenerate and occurs along a ring in $(k_x,k_y)$ space. This reduces the effective dimensionality; the single-particle density of states is a constant at low energies, and the molecular pairing is strongly enhanced. In contrast to the continuum, in the 2D lattice case there are only four degenerate minima, 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 are 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 the small fillings and weak attraction limit. Moreover, we found that the speed of sound also exhibits different behavior: in the 3D and 2D continuum, 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 SOC strength.