Decoherence of Coupled Quantum Oscillators: Going Beyond the Caldeira-Leggett Approximation

TL;DR

This paper investigates how coupled quantum oscillators decohere in different heat bath configurations, revealing unique dissipation mechanisms and reservoir-induced interactions beyond traditional models.

Contribution

It extends the analysis of quantum decoherence by exploring coupled oscillators interacting with separate or common reservoirs, highlighting differences from the Caldeira-Leggett approximation.

Findings

Distinct dissipation mechanisms identified for common vs. separate reservoirs

Reservoir-induced interactions can emerge in coupled systems

Classical-like evolution of position and momentum expectation values

Abstract

We calculate the reduced density matrix for a system of coupled harmonic oscillators in a bosonic heat bath using the Born-Markov approximation and show that the expectation values of position and momentum evolve like classical quantities. We consider the cases where every oscillator is coupled to its own reservoir and where all oscillators are coupled to the same heat bath, pointing out the differences between these two models. In particular, for systems coupled to a common reservoir, we present an uncommon dissipation mechanism, which disappears, when the dynamics of the system are gouverned by the low frequency modes of the environment (Caldeira-Leggett limit). We also address the interesting phenomenon of reservoir-induced interactions.