Abstract
We model the cooling of open optical and optomechanical resonators via optical feedback in the linear quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible linear quadratic Gaussian measurement-based schemes in the quantum regime of low steady-state excitation number. Such performance gains are attributed to the coherent controller's ability to process noncommuting output field quadratures simultaneously without loss of fidelity, and may provide important clues for the design of coherent feedback schemes for more general problems of nonlinear and robust control.
Highlights
We model the cooling of open optical and optomechanical resonators via optical feedback in the linear quadratic Gaussian setting of stochastic control theory
We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible linear quadratic Gaussian measurement-based schemes in the quantum regime of low steady-state excitation number
James, Nurdin, and Petersen [22,23] have utilized interconnection models [24,25,26] based on quantum stochastic differential equations [27,28,29] to develop generalizations of the traditional H 1 and linear quadratic Gaussian (LQG) control paradigms that allow for the possibility of coherent optical feedback with linear quantum controllers
Summary
We model the cooling of open optical and optomechanical resonators via optical feedback in the linear quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible linear quadratic Gaussian measurement-based schemes in the quantum regime of low steady-state excitation number. James, Nurdin, and Petersen [22,23] have utilized interconnection models [24,25,26] based on quantum stochastic differential equations [27,28,29] to develop generalizations of the traditional H 1 and linear quadratic Gaussian (LQG) control paradigms that allow for the possibility of coherent optical feedback with linear quantum controllers.
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