Entanglement Structure of an Open System of $N$ Quantum Oscillators: II. Strong Disparate Couplings N=3

TL;DR

This paper investigates the entanglement structure of three coupled quantum oscillators interacting with a quantum field, analyzing how disparate coupling strengths influence quantum correlations at a stationary state.

Contribution

It provides a detailed analysis of entanglement in a three-oscillator system with varying coupling strengths using the influence functional formalism and covariance matrix methods.

Findings

Entanglement varies with symmetric and asymmetric couplings.

Disparate couplings significantly affect quantum correlations.

Results applicable to quantum thermodynamics and mesoscopic systems.

Abstract

In this paper we study a system of $N$ coupled quantum oscillators interacting with each other directly with varying coupling strengths and indirectly through linear couplings to a scalar massless quantum field as its environment. The influence of the quantum field on the system is calculated with the use of the influence functional formalism. We take the direct route of seeking solutions to the evolutionary operator of the reduced density matrix for the derivation of the correlation functions. They are then used to construct the covariance matrix which we use to perform an analysis of the structure of quantum entanglement in the open system at a stationary state. To see the physical features more explicitly we specialize to a system of three quantum coupled oscillators placed at the vertices of a equilateral triangle and allowed to have disparate pairwise couplings. We analyze the entanglement between one oscillator and the other two with equal (symmetric) and unequal (asymmetric) coupling strengths. As an illustration we use the results for these two different configurations to address two representative issues in macroscopic quantum phenomena. We also mention possible extensions of our work and applications of our analysis and results to issues in some current areas of research in quantum thermodynamics and mesoscopic quantum systems.