Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems

TL;DR

This paper introduces an efficient numerical method based on a stochastic extension of the discrete truncated Wigner approximation to simulate large, dissipative spin ensembles, capturing quantum correlations and nonclassical effects without symmetry assumptions.

Contribution

The authors develop a generalized stochastic discrete truncated Wigner method for dissipative spin systems, enabling large-scale, realistic simulations of quantum optical and solid-state spin experiments.

Findings

Simulated nonclassical spin-squeezing effects.

Analyzed steady states of cavity QED models with hundreds of thousands of spins.

Achieved accurate simulations without relying on symmetries.

Abstract

We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which combines the mean-field dynamics of a spin ensemble with a Monte Carlo sampling of discrete initial spin values to account for quantum correlations. Here we show how this approach can be generalized for dissipative spin systems by replacing the deterministic mean-field evolution by a stochastic process, which describes the decay of coherences and populations while preserving the length of each spin. We demonstrate the application of this technique for simulating nonclassical spin-squeezing effects or the dynamics and steady states of cavity QED models with hundred thousand interacting two-level systems and without relying on any symmetries. This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.