Focused Sampling for Low-Cost and Accurate Ehrenfest Modeling of Cavity Quantum Electrodynamics

TL;DR

This paper introduces a focused sampling method combined with decoupled mean-field dynamics to improve the accuracy and efficiency of Ehrenfest modeling in cavity quantum electrodynamics, addressing energy leakage and convergence issues.

Contribution

It presents an integrated approach that enhances Ehrenfest dynamics with focused sampling and a modified theorem, reducing trajectories needed and improving accuracy in various cavity regimes.

Findings

Achieves high accuracy in short and long-cavity limits

Requires fewer trajectories for convergence

Addresses zero-point energy leakage effectively

Abstract

An economic modeling approach for cavity quantum electrodynamics is provided by mean-field dynamics, wherein the optical field is described classically while a self-consistent interaction with quantum emitters is incorporated through the Ehrenfest theorem. However, conventional implementations of mean-field dynamics are known to suffer from a catastrophic leakage of zero-point energy, to lose accuracy in the short-cavity limit, and to require large numbers of trajectories to be sampled. Here, we address these three shortcomings within a single integrated approach. This approach builds on our recently-proposed modification of the Ehrenfest theorem, referred to as decoupled mean-field (DC-MF) dynamics, in combination with a focused sampling scheme that enforces zero-point energy at the single-trajectory level. The approach is shown to yield high accuracy in both short and long-cavity limits while reaching convergence within a minimal amount of trajectories.