Evolution of a quantum harmonic oscillator coupled to a minimal thermal environment

TL;DR

This study investigates how a minimal thermal environment, modeled as a second oscillator, influences the dynamics and decoherence of a quantum harmonic oscillator, comparing exact evolution with traditional master equation approaches.

Contribution

It introduces a minimal model of a thermal environment using a second oscillator and compares its effects on decoherence with standard reservoir models.

Findings

Simplified models can capture key features of decoherence.

The evolution of linear entropy reveals insights into decoherence mechanisms.

Comparison shows differences between minimal and large reservoir environments.

Abstract

In this paper it is studied the influence of a minimal thermal environment on the dynamics of a quantum harmonic oscillator (labelled A), prepared in a coherent state. The environment itself consists of a second oscillator (labelled B), initially in a thermal state. Two types of interaction Hamiltonians are considered, and the time-evolution of the reduced density operator of oscillator A is compared to the one obtained from the usual master equation approach, i.e., assuming that oscillator A is coupled to a large reservoir. An analysis of the linear entropy evolution of oscillator A shows that simplified models may be able to describe important features related to the phenomenon of decoherence.