Dynamics of the inhomogeneous Dicke model

TL;DR

This paper analyzes the time evolution of a boson interacting with inhomogeneous two-level systems, revealing how decay dynamics vary from oscillatory to exponential depending on inhomogeneity levels.

Contribution

It provides an exact analysis of the inhomogeneous Dicke model's dynamics, characterizing decay behaviors across different inhomogeneity regimes.

Findings

At resonance, boson decays to an oscillatory state with a finite amplitude.

Decay behavior transitions from suppressed to exponential as inhomogeneity increases.

Intermediate inhomogeneity results in partial decay governed by combined exponential and power laws.

Abstract

We study the time dynamics of a single boson coupled to a bath of two-level systems (spins 1/2) with different excitation energies, described by an inhomogeneous Dicke model. Analyzing the time-dependent Schrodinger equation exactly we find that at resonance the boson decays in time to an oscillatory state with a finite amplitude characterized by a single Rabi frequency if the inhomogeneity is below a certain threshold. In the limit of small inhomogeneity, the decay is suppressed and exhibits a complex (mainly Gaussian-like) behavior, whereas the decay is complete and of exponential form in the opposite limit. For intermediate inhomogeneity, the boson decay is partial and governed by a combination of exponential and power laws.