Spontaneous polarized phase transitions and symmetry breaking of an ultracold atomic ensemble in a Raman-assisted cavity

TL;DR

This paper explores the quantum phase transitions and symmetry breaking in an ultracold atomic ensemble within a Raman-assisted cavity, revealing novel polarized phases and a complex symmetry structure governed by Coxeter groups.

Contribution

It introduces an extended imbalanced Dicke model with novel polarized phases and a detailed phase diagram, including multiple symmetries and their breaking or restoration.

Findings

Identification of novel polarized phases with phase differences.

Full phase diagram and quantum phase transition analysis.

Discovery of multiple symmetries governed by Coxeter groups.

Abstract

We investigate the ground-state properties and quantum phase transitions of an ensemble consisting of $N$ four-level atoms within an optical cavity coupled to the single cavity mode and external laser fields. The system is described by an extended imbalanced Dicke model, in which the co- and counterrotating coupling terms are allowed to have different coupling strengths. Some novel polarized phases characterized by the phase differences between the cavity field or the atomic spin excitation and the Raman laser are found analytically. Meanwhile, the full phase diagram and quantum phase transitions are also revealed. Finally, the breaking or restoration of the intrinsic symmetry in this system is addressed. It is found that besides the continuous $U(1)$ and discrete $\mathbb{Z}_2$ symmetries, the system also exhibits two reflection symmetries $\sigma_v$s, a central symmetry $C_2$ in the abstract position-momentum representation, and a discrete reflection parity-time ($\mathcal{PT}$) symmetry, a parameter exchange symmetry $\mathcal{T}_\mathrm{ex}$ in the parameters space. These additional symmetries are governed by two Coxeter groups.