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arXiv · 2502.12305

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

Aniket Patra·Felix Motzoi·Klaus Mølmer
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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.

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Aniket Patra, Felix Motzoi, Klaus Mølmer. 2025-02-17. Stochastic Schr\"{o}dinger equation for a homodyne measurement setup of strongly correlated systems. https://doi.org/10.1088/1361-6455%2Fae0bd2

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