Pairing sizes in attractively interacting Fermi gases with Spin-orbit Couplings

TL;DR

This paper investigates how spin-orbit coupling influences the BCS to BEC crossover in Fermi gases, identifying the pairing length as a key measurable quantity that characterizes this transition.

Contribution

It extends the concepts of pairing length and Cooper-pair size to systems with spin-orbit coupling and demonstrates the pairing length's unique role in describing the crossover.

Findings

Pairing length uniquely characterizes the new BCS to BEC crossover with SOC.

Only the pairing length can be directly measured via radio-frequency dissociation spectra.

Differences among pairing length, Cooper-pair size, and two-body bound state size are clarified.

Abstract

Extensive research has been lavished on effects of spin-orbit couplings (SOC) in attractively interacting Fermi systems in both neutral cold atom systems and condensed matter systems. Recently, it was suggested that a SOC drives a new class of BCS to BEC crossover which is different than the conventional one without a SOC. Here, we explore what are the most relevant physical quantities to describe such a new BCS to BEC crossover and their experimental detections. We extend the concepts of the pairing length and "Cooper-pair size" in the absence of SOC to Fermi systems with SOC. We investigate the dependence of chemical potential, pairing length, "Cooper-pair size" on the SOC strength and the scattering length at $ 3d $ (the bound state energy at $ 2d $) for three attractively interacting Fermi gases with 3 dimensional (3d) Rashba, 3d Weyl and 2d Rashba SOC respectively. We show that only the pairing length can be used to characterize this new BCS to BEC crossover. Furthermore, it is the only length which can be directly measured by radio-frequency dissociation spectra type of experiments. We stress crucial differences among the pairing length, "Cooper-pair size " and the two-body bound state size. Our results provide the fundamental and global picture of the new BCS to BEC crossover and its experimental detections in various cold atom and condensed matter systems.