Continuous measurements on continuous variable quantum systems: The Gaussian description

TL;DR

This paper develops an efficient Gaussian state formalism for modeling the quantum interaction between macroscopic atomic samples and continuous light beams, enabling analysis of spin squeezing and parameter estimation.

Contribution

It introduces a differential equation-based Gaussian description that accounts for dynamics, dissipation, noise, and measurement back-action in atom-light interactions.

Findings

Effective modeling of atomic spin squeezing.

Quantitative analysis of parameter estimation.

Framework applicable beyond Gaussian states.

Abstract

The Gaussian state description of continuous variables is adapted to describe the quantum interaction between macroscopic atomic samples and continuous-wave light beams. The formalism is very efficient: a non-linear differential equation for the covariance matrix of the atomic system explicitly accounts for both the unitary evolution, the dissipation and noise due to the atom-light interaction, and the back-action due to homodyne optical detection on the beam after its interaction with the atoms. Applications to atomic spin squeezing and estimation of unknown classical parameters are presented, and extensions beyond the Gaussian states are discussed.