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Communications on Pure and Applied Mathematics

A time‐dependent approach to the completeness of multiparticle quantum systems

Percy A. Deift, Barry Simon A

Published Sep 1, 1977• 43 citations
Publisher
DOI
10.1002/cpa.3160300504

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Recent developments in quantum gas microscopy open up the possibility of real-time observation of quantum many-body systems. To understand the dynamics of atoms under such circumstances, we formulate the dynamics under a real-time spatially resolved measurement and show that, in an appropriate limit of weak spatial resolution and strong atom-light coupling, the measurement indistinguishability of particles results in complete suppression of relative positional decoherence. As a consequence, quantum correlation in the multiparticle dynamics persists under a minimally destructive observation. We numerically demonstrate this for ultracold atoms in an optical lattice. Our theoretical framework can be applied to the feedback control of quantum many-body systems which may be realized in subwavelength-spacing lattice systems.