Stochastic Schrödinger equation for a homodyne measurement setup of strongly correlated systems

• URL: http://arxiv.org/abs/2502.12305v2
• Date: Thu, 03 Jul 2025 13:30:09 GMT
• Title: Stochastic Schrödinger equation for a homodyne measurement setup of strongly correlated systems
• Authors: Aniket Patra, Felix Motzoi, Klaus Mølmer,
• Abstract summary: We numerically study the Bose-Hubbard model under continuous observation.<n>We show that time-domain analysis of the measurement signal uncovers rich dynamical features, including quantum jumps, that are obscured in ensemble-averaged spectral data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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