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

TL;DR

This work addresses superradiant phase transitions of a one-dimensional correlated Fermi gas under cavity-induced umklapp scattering by mapping the low-energy physics to an all-to-all sine-Gordon model via bosonization and analyzing it with renormalization group methods. The main result is that the nesting effect drives the critical coupling to zero for nonattractive local interactions ($g<1$), while attractive interactions yield a finite critical coupling; the nonlocal cosine term has a scaling dimension $d=2g$ with an upper critical dimension $d_c=2$, yielding KT-type behavior despite long-range coupling. The analysis provides a coherent analytical framework for understanding intracavity low-dimensional Fermi gases and clarifies how nonlocal cavity-mediated interactions interplay with fermionic correlations. These insights have implications for experiments in cavity QED systems and connect to broader contexts of long-range sine-Gordon models and BCS–BEC crossover physics.

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.

Figures (2)

• Figure 1: Illustration of the model. The 1D Fermi gas is coupled with the cavity field ($\Omega_{c}$) via a transverse driving ($\Omega_{p}$). The atoms are assumed to have two energy levels (not shown), and the higher level has been adiabatically eliminated since the driving and cavity fields are far detuning from the energy levels. The Fermi surface (FS) is assumed to be resonant with the cavity field, i.e., $k_{0}=2k_{f}$.
• Figure 2: Phase diagram. The bold red line denotes the unstable fixed points on the negative semiaxis of $z_{\perp}$, which corresponds to the quantum phase transition with vanishing coupling strength. The red dashed curve marks the marginal curve of relevant regime, which separates the massive (M) phase (gray shade) and critical (C) phase (yellow shade). In phase M (C) the system has finite (vanishing) mass gap. The red circle indicates the nesting effect (infinitely small critical coupling strength) in free Fermi gases predicted with the Landau theory of phase transition piazza2014umklappkeeling2014fermionicchen2014superradiance. The phase diagram shows that the nesting effect survives for non-attractive local interactions ($g<1$) only.