Stochastic Mean-field Theory for Conditional Spin Squeezing by Homodyne Probing of Atom-Cavity Photon Dressed States

TL;DR

This paper introduces a stochastic cumulant mean-field theory for analyzing conditional spin squeezing in large atom-cavity systems, providing an efficient alternative to existing methods and enabling the study of complex quantum measurement effects.

Contribution

It develops a stochastic cumulant mean-field approach for large quantum systems, validated against exact methods, and demonstrates its application to spin squeezing in atom-cavity setups.

Findings

Accurately simulates spin squeezing in thousands of atoms.

Shows the method's effectiveness compared to exact stochastic density matrix simulations.

Reveals formation and detection of spin squeezed states in experimental protocols.

Abstract

Projective measurements of collective observables can be employed to herald the preparation of entangled states of quantum systems, and the resulting conditional dynamics is usually handled by stochastic master equation (SME) for small systems, and by an approximate Gaussian-state formalism for large systems. In this work, we present an alternative technique by developing a stochastic variant of cumulant mean-field theory, benchmark it against an exact stochastic collective density matrix approach by the simulations of hundreds of identical two-level atoms. More importantly, we demonstrate its full power by studying the conditional spin squeezing of thousands of three-level atoms coupled strongly with an optical cavity subject to individual decay and dephasing, and by simulating the experimental protocol to reveal formation and detection of the spin squeezed state. The proposed technique might be further extended to study more exotic quantum-measurement effects of large quantum systems, such as deterministic spin squeezing with quantum feedback, spin squeezing of optical clock transitions, and retrodictive spin squeezing by posterior measurements, and so on.