Quantum phases of a two-dimensional polarized degenerate Fermi gas in an optical cavity

TL;DR

This paper analytically explores the ground-state quantum phases of a two-dimensional polarized degenerate Fermi gas in an optical cavity, revealing rich phase diagrams influenced by various tunable parameters and predicting coexistence phases and phase transitions.

Contribution

It introduces a generalized Fermi-Dicke model for the system and analytically characterizes multiple quantum phases and phase transitions, including coexistence of superfluid, superradiant, and normal phases.

Findings

Identification of a mixed phase with normal and superradiant states without fermion-fermion interaction.

Prediction of a phase transition from normal to superradiant phase.

Discovery of a coexistence phase of superfluid and superradiant states under certain conditions.

Abstract

In this paper we analytically investigate the ground-state properties of a two-dimensional polarized degenerate Fermi gas in a high-finesse optical cavity, which is governed by a generalized Fermi-Dicke model with tunable parameters. By solving the photon-number dependent Bogoliubov-de-Gennes equation, we find rich quantum phases and phase diagrams, which depend crucially on the fermion-photon coupling strength, the fermion-fermion interaction strength, and the atomic resonant frequency (effective Zeeman field). In particular, without the fermion-fermion interaction and with a weak atomic resonant frequency, we find a mixed phase that the normal phase with two Fermi surfaces and the superradiant phase coexist, and reveal a first-order phase transition from this normal phase to the superradiant phase. With the intermediate fermion-fermion interaction and fermion-photon coupling strengths, we predict another mixed phase that the superfluid and superradiant phases coexist. Finally, we address briefly how to detect these predicted quantum phases and phase diagrams in experiments.