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Physics Letters A

Solvable model of quantum-optical feedback

V. A. Tomilin, Leonid V. Il'ichov

Published Jul 9, 2020• 1 citation
Publisher
DOI
10.1016/j.physleta.2020.126718

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A quantized optical cavity mode controlled by dissipation, squeezed-light source and feedback loop is studied. The feedback is activated by detections of photons leaving the cavity and rapidly shifts the phase of the cavity field by π. The steady-state of the mode and first-order field correlation functions are obtained in closed analytical form and investigated. It appears that the feedback radically modifies the mode's spectrum. It gains asymmetry and its double-peaked structure becomes much more pronounced than in no-feedback case.
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic control theory, we present the theory of nonlinear optimal quantum feedback control. The resulting quantum Bellman equation is then applied to the explicitly solvable quantum linear-quadratic-Gaussian (LQG) problem which emphasizes many similarities with the corresponding classical control problem.