Temperature effects on a network of dissipative quantum harmonic oscillators: collective damping and diffusion processes

TL;DR

This paper investigates how finite temperature reservoirs influence the dynamics, decoherence, and entanglement in a network of coupled quantum harmonic oscillators, providing master equations and analyzing collective diffusion effects.

Contribution

It extends previous models to include finite temperature effects and analyzes both individual and common reservoirs in a bosonic dissipative network.

Findings

Derived master equations for different reservoir configurations and coupling regimes.

Presented solutions using the normal ordered characteristic function.

Analyzed diffusion, decoherence, and entanglement dynamics in the network.

Abstract

In this article we extend the results presented in Ref. [Phys. Rev. A 76, 032101 (2007)] to treat quantitatively the effects of reservoirs at finite temperature in a bosonic dissipative network: a chain of coupled harmonic oscillators whichever its topology, i.e., whichever the way the oscillators are coupled together, the strength of their couplings and their natural frequencies. Starting with the case where distinct reservoirs are considered, each one coupled to a corresponding oscillator, we also analyze the case where a common reservoir is assigned to the whole network. Master equations are derived for both situations and both regimes of weak and strong coupling strengths between the network oscillators. Solutions of these master equations are presented through the normal ordered characteristic function. We also present a technique to estimate the decoherence time of network states by computing separately the effects of diffusion and the attenuation of the interference terms of the Wigner function. A detailed analysis of the diffusion mechanism is also presented through the evolution of the Wigner function. The interesting collective diffusion effects are discussed and applied to the analysis of decoherence of a class of network states. Finally, the entropy and the entanglement of a pure bipartite system are discussed.