Modelling many-body quantum dynamics with stochastic trajectories: a critical test on the Tavis-Cummings model

TL;DR

This paper critically evaluates a stochastic trajectory framework for simulating many-body quantum light-matter interactions, revealing divergence issues and limitations in capturing quantum phenomena like collapse and revival in the Tavis-Cummings model.

Contribution

It provides a detailed analysis of the applicability and limitations of stochastic phase-space methods for many-body quantum dynamics, especially in the Tavis-Cummings model.

Findings

Divergences in stochastic differential equations limit simulation times.

Transforming SDEs can extend valid simulation periods.

Quantum collapse and revival are not captured by the stochastic approach.

Abstract

We critically explore the applicability of a recently proposed framework to sample the quantum dynamics of a many-body quantum system interacting with light by stochastic trajectories, applying it to the closed and open Tavis-Cummings model (TCM). The stochastic differential equations (SDEs) sample the positive P phase-space representation by analog complex-valued dynamical variables that are linked to the quantum operators. Statistical average over the stochastic trajectories yields the evolution of the quantum mechanical expectation values. However, numerical implementation of these SDEs for the TCM indicates divergent solutions, also known from other phase-space methods. This limits the applicability of the framework to finite propagation times, that are strongly dependent on the physical parameters and initial conditions of the system. We outline the underlying mathematical reason for these divergences and show that their contribution to the averages are, however, essential. To attempt to regularize the divergences, we transform the SDEs to an equivalent set of SDEs with different noise realisations, thereby pushing the valid time boundary. Quantum collapse and revival of the TCM, however, cannot be recovered by the stochastic trajectory approach, pointing to the general difficulty of the applicability of stochastic phase-space sampling methods to systems with strong quantum features.