Stochastic Schrödinger equation for homodyne measurements of strongly correlated systems

• URL: http://arxiv.org/abs/2502.12305v1
• Date: Mon, 17 Feb 2025 20:26:39 GMT
• Title: Stochastic Schrödinger equation for homodyne measurements of strongly correlated systems
• Authors: Aniket Patra, Felix Motzoi, Klaus Mølmer,
• Abstract summary: We derive a Schr"odinger equation that describes the homodyne measurement record of a strongly interacting atomic system. We then demonstrate that the derived equation for this setup in the appropriate limit is the same as the one obtained while performing a Gaussian quantum continuous measurement.
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• Abstract: We derive a stochastic Schr\"{o}dinger equation that describes the homodyne measurement record of a strongly interacting atomic system. We derive this equation for a general system, where we use the rotating wave approximation in the linear atom-light interaction part, and the resulting equation is expressed in terms of the atomic operators only. Weak measurements are theoretically described in terms of positive operator-valued measures. Among different weak measurement schemes, several earlier references studied the Gaussian quantum continuous measurement in detail. Here we consider a homodyne measurement setup. We then demonstrate that the derived equation for this setup in the appropriate limit is the same as the one obtained while performing a Gaussian quantum continuous measurement.

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