Universal four-component Fermi gas in one dimension

TL;DR

This paper explores a one-dimensional four-component Fermi gas with short-range four-body interactions, revealing a BCS-BEC crossover, spin gaps, and universal few-body phenomena, including an Efimov effect for bosons.

Contribution

It introduces the first analysis of a 1D four-component Fermi gas exhibiting a BCS-BEC crossover and universal few-body effects, expanding understanding of low-dimensional quantum systems.

Findings

Identification of a BCS-BEC crossover in 1D four-component Fermi gas

Discovery of exponentially small and large spin gaps in different regimes

Observation of a 1D Efimov effect for five bosons

Abstract

A four-component Fermi gas in one dimension with a short-range four-body interaction is shown to exhibit a one-dimensional analog of the BCS-BEC crossover. Its low-energy physics is governed by a Tomonaga-Luttinger liquid with three spin gaps. The spin gaps are exponentially small in the weak coupling (BCS) limit where they arise from the charge-density-wave instability, and become large in the strong coupling (BEC) limit because of the formation of tightly-bound tetramers. We investigate the ground-state energy, the sound velocity, and the gap spectrum in the BCS-BEC crossover and discuss exact relationships valid in our system. We also show that a one-dimensional analog of the Efimov effect occurs for five bosons while it is absent for fermions. Our work opens up a very rich new field of universal few-body and many-body physics in one dimension.