Quantum correlations for two coupled oscillators interacting with two heat baths

TL;DR

This paper investigates the quantum correlations of two coupled oscillators each interacting with its own heat bath, showing that the system remains separable over time and analyzing its equilibrium state using Gaussian state formalism.

Contribution

The study demonstrates that the two coupled oscillators maintain separability at all times and provides a detailed analysis of their equilibrium Wigner function.

Findings

The two oscillators' state remains separable throughout evolution.

The equilibrium state is characterized by a specific Wigner function.

The system's dynamics do not generate entanglement between the oscillators.

Abstract

We study a system of two coupled oscillators (the $A$ oscillator) each of the oscillators linearly interacts with its own heat bath consisting of a set of independent harmonic oscillators (the $B$ oscillators). The initial state of the $A$ oscillator is taken to be coherent while the $B$ oscillators are in thermal states. We analyze the time-dependent state of the $A$ oscillator which is a two-mode Gaussian state. By making use of Simon's separability criterion we show that this state is separable for all times. We consider the equilibrium state of the $A$ oscillator in detail and calculate its Wigner function.