Dynamical properties of the Rabi model

TL;DR

This paper investigates the dynamical behavior of the quantum Rabi model using a systematic expansion method that leverages parity symmetry to analyze state evolution.

Contribution

It introduces a novel expansion approach based on parity symmetry to study the dynamics of the quantum Rabi model.

Findings

Decomposition of states into positive and negative parity components.

Derivation of recurrence relations for expansion coefficients.

Analytical expressions for state evolution in the Rabi model.

Abstract

We study the dynamical properties of the quantum Rabi model within a systematic expansion method. Based on the observation that the parity symmetry of the Rabi model is kept during the evolution of the states, we decompose the initial state and the time-dependent one into a part of a positive and a negative parity expanded by the superposition of the coherent states. The evolutions for the corresponding positive and the negative parity are obtained, where the expansion coefficients in the dynamical equations are known from the recurrence relation derived.