Gaussian Quantum Trajectories for the Variational Simulation of Open Quantum-Optical Systems

TL;DR

This paper introduces Gaussian variational methods for simulating open quantum optical systems, providing a balance of computational efficiency and accuracy, especially in complex regimes like bistability.

Contribution

The authors develop a novel Gaussian trajectory-based variational approach that improves upon existing methods in simulating open quantum systems.

Findings

Methods have similar computational cost to TWA.

Strong correspondence with exact trajectory methods.

More robust and informative than traditional TWA.

Abstract

We construct a class of variational methods for the study of open quantum systems based on Gaussian ansatzes for the quantum trajectory formalism. Gaussianity in the conjugate position and momentum quadratures is distinguished from Gaussianity in density and phase. We apply these methods to a driven-dissipative Kerr cavity where we study dephasing and the stationary states throughout the bistability regime. Computational cost proves to be similar to the truncated Wigner (TWA) method, with at most quadratic scaling in system size. Meanwhile, strong correspondence with the numerically exact trajectory description is maintained so that these methods contain more information on the ensemble constitution than TWA and can be more robust.