Heat transport in harmonic oscillator systems with correlated baths: Application to optomechanical arrays

TL;DR

This paper studies phonon heat transport in harmonic oscillator systems with correlated baths, applying the theory to optomechanical arrays to understand steady state heat flow and occupation numbers.

Contribution

It derives a general expression for steady state heat flow in harmonic oscillators with correlated baths and applies it to optomechanical arrays, revealing new insights into their thermal behavior.

Findings

Steady state heat flow expression for oscillators with correlated baths.

Optomechanical array behavior analogous to coupled oscillators with an effective bath.

Analysis of occupation numbers and heat flows in various regimes.

Abstract

We investigate the transport of phonons between $N$ harmonic oscillators in contact with independent thermal baths and coupled to a common oscillator, and derive an expression for the steady state heat flow between the oscillators in the weak coupling limit. We apply these results to an optomechanical array consisting of a pair of mechanical resonators coupled to a single quantised electromagnetic field mode by radiation pressure as well as to thermal baths with different temperatures. In the weak coupling limit this system is shown to be equivalent to two mutually-coupled harmonic oscillators in contact with an effective common thermal bath in addition to their independent baths. The steady state occupation numbers and heat flows are derived and discussed in various regimes of interest.