Superradiant phase transitions in one-dimensional correlated Fermi gases with cavity-induced umklapp scattering

TL;DR

This paper investigates superradiant phase transitions in one-dimensional correlated Fermi gases within an optical cavity, revealing a mapping to a Kosterlitz-Thouless transition and highlighting the effects of interactions and umklapp scattering.

Contribution

It introduces an analytical framework using bosonization and RG techniques to study superradiant transitions in correlated Fermi gases with cavity-induced umklapp scattering, including all-to-all sine-Gordon modeling.

Findings

Superradiant transition maps to Kosterlitz-Thouless transition.

Nesting effect allows infinitesimal coupling to trigger transition.

Phase transition behavior depends on local interaction attractiveness.

Abstract

The superradiant phase transitions of one-dimensional correlated Fermi gases in a transversely driven optical cavity, under the umklapp condition that the cavity wave number is equal to two times the Fermi wave number, are studied with bosonization and renormalization group techniques. The bosonization of Fermi fields gives rise to an all-to-all sine-Gordon (SG) model due to the cavity-assisted nonlocal interactions, where the Bose fields at any two spatial points are coupled. The superradiant phase transition is then mapped to the Kosterlitz-Thouless phase transition of the all-to-all SG model. The nesting effect, in which the superradiant phase transition can be triggered by an infinitely small atom-cavity coupling strength, is shown to be preserved for any nonattractive local interactions. For attractive local interactions, the phase transition occurs at a finite critical coupling strength. Nevertheless, the analysis of the scaling dimension indicates that the perturbation of the nonlocal cosine term is indeed relevant (irrelevant) when the scaling dimension is lower (higher) than the critical dimension, similar to the case of an ordinary local SG model. Our work provides an analytical framework for understanding the superradiant phase transitions in low-dimensional correlated intracavity Fermi gases.