BCS-BEC crossover in spin-orbit coupled two-dimensional Fermi gases

TL;DR

This paper explores the BCS-BEC crossover in two-dimensional spin-orbit coupled Fermi gases, providing analytical and numerical insights into ground state properties and how they are affected by spin-orbit coupling strength.

Contribution

It presents the first detailed analysis of 2D spin-orbit coupled Fermi gases, deriving analytic expressions for key ground state quantities and comparing them with numerical results.

Findings

Chemical potential shifts with SOC strength.

Superfluid gap increases significantly in BCS limit with strong SOC.

Analytic results agree with numerical data across broad parameters.

Abstract

The recent experimental realization of spin-orbit coupling for ultra-cold atoms has generated much interest in the physics of spin-orbit coupled degenerate Fermi gases. Although recently the BCS-BEC crossover in three-dimensional (3D) spin-orbit coupled Fermi gases has been intensively studied, the corresponding two-dimensional (2D) crossover physics has remained unexplored. In this paper, we investigate, both numerically and analytically, the BCS-BEC crossover physics in 2D degenerate Fermi gases in the presence of a Rashba type of spin-orbit coupling. We derive the mean field gap and atom number equations suitable for the 2D spin-orbit coupled Fermi gases and solve them numerically and self-consistently, from which the dependence of the ground state properties (chemical potential, superfluid pairing gap, ground state energy per atom) on the system parameters (e.g., binding energy, spin-orbit coupling strength) is obtained. Furthermore, we derive analytic expressions for these ground state quantities, which agree well with our numerical results within a broad parameter region. Such analytic expressions also agree qualitatively with previous numerical results for the 3D spin-orbit coupled Fermi gases, where analytic results are lacked. We show that with an increasing SOC strength, the chemical potential is shifted by a constant determined by the SOC strength. The superfluid pairing gap is enhanced significantly in the BCS limit for strong SOC, but only increases slightly in the BEC limit.