Stochastic Schr\"{o}dinger equation for a homodyne measurement setup of strongly correlated systems

TL;DR

This paper derives a stochastic Schr"{o}dinger equation for homodyne detection of strongly correlated atomic systems, enabling detailed analysis of quantum dynamics and jumps in continuous measurement scenarios.

Contribution

It introduces a reduced stochastic Schr"{o}dinger equation applicable to strongly interacting systems under homodyne detection, bridging experimental setups with idealized quantum measurement theory.

Findings

Numerical simulation of the Bose-Hubbard model reveals quantum jumps and rich dynamics.

The derived equation simplifies the analysis of continuous measurements in complex quantum systems.

Time-domain signals provide insights obscured in spectral averages.

Abstract

Starting from an experimentally feasible atomic setup, we derive a stochastic Schr\"{o}dinger equation that captures the homodyne detection record of a strongly interacting system. Applying the rotating wave approximation to the linear atom-light coupling, we arrive at a reduced equation formulated solely in terms of atomic operators. In the appropriate limit, this equation converges to that of Gaussian continuous quantum measurement -- revealing that the complexities of real-world detection can, under certain conditions, echo the elegance of idealized theory. To illustrate the utility of this framework, we numerically study the Bose-Hubbard model under continuous observation, showing that time-domain analysis of the measurement signal uncovers rich dynamical features, including quantum jumps, that are obscured in ensemble-averaged spectral data.