Correlator expansion approach to stationary states of weakly coupled cavity arrays

TL;DR

This paper presents a correlator expansion method to efficiently compute the stationary states of weakly coupled cavity arrays, capturing strong correlations and nonlinear effects without full density matrix calculations.

Contribution

The paper introduces a second-order correlator expansion technique for analyzing stationary states in weakly coupled cavity arrays, applicable to large systems with strong nonlinearities.

Findings

Exact second-order solutions for any number of cavities.

Effective for strongly correlated, nonlinear regimes.

Provides a controllable approximation for weak tunneling.

Abstract

We introduce a method for calculating the stationary state of a translation invariant array of weakly coupled cavities in the presence of dissipation and coherent as well as incoherent drives. Instead of computing the full density matrix our method directly calculates the correlation functions which are relevant for obtaining all local quantities of interest. It considers an expansion of the correlation functions and their equations of motion in powers of the photon tunneling rate between adjacent cavities, leading to an exact second order solution for any number of cavities. Our method provides a controllable approximation for weak tunneling rates applicable to the strongly correlated regime that is dominated by nonlinearities in the cavities and thus of high interest.