Dissecting the superradiant phase transition in the anisotropic Rabi model: Pattern competition and cavity-QED simulation

TL;DR

This paper investigates the superradiant phase transition in the anisotropic Rabi model using pattern analysis, revealing that phase transition results from pattern competition and can be simulated via a parametrically-driven Jaynes-Cummings model.

Contribution

It introduces a pattern-based analysis of the anisotropic Rabi model and connects it to a quantum simulation using a parametrically-driven Jaynes-Cummings model.

Findings

Phase transition arises from competition between three patterns.

Eigenenergies vanish at the critical point, indicating a phase transition.

Photon number diverges beyond the critical point.

Abstract

In this manuscript, we analyze the mechanism of the superradiant phase transition in the anisotropic Rabi model under the classical oscillator limit using the pattern picture. By expanding the anisotropic Rabi model Hamiltonian in operator space, we obtained three patterns, and we find that the phase transition arises from the competition between patterns. The difficulty in achieving the classical oscillator limit motivates our investigation into the quantum phase transition within a parametrically-driven Jaynes-Cummings model. This parametrically-driven Jaynes-Cummings model can reproduce the dynamics of an ultrastrong-coupling anisotropic Rabi model in a squeezed-light frame. According to the eigenenergies and eigenstates of the normal and superradiant phases of this equivalent anisotropic Rabi model, we find that the excitation energy of the normal phase and the superradiant phase vanishes at the critical point. The photon number becomes infinite beyond the critical point. These results indicate that the system undergoes a superradiant phase transition at the critical point.