Abstract
We study the cooling performance of optical-feedback controllers for open optical and mechanical resonators in the Linear Quadratic Gaussian setting of stochastic control theory. We utilize analysis and numerical optimization of closed-loop models based on quantum stochastic differential equations to show that coherent control schemes, where we embed the resonator in an interferometer to achieve all-optical feedback, can outperform optimal measurement-based feedback control schemes in the quantum regime of low steady-state excitation number. These performance gains are attributed to the coherent controller's ability to simultaneously process both quadratures of an optical probe field without measurement or loss of fidelity, and may guide the design of coherent feedback schemes for more general problems of robust nonlinear and robust control.
Highlights
As present-day engineering relies broadly and implicitly on real-time feedback control methodology [1], it is difficult to imagine our nascent explorations of quantum engineering advancing to technological relevance without rigorous extensions of core control theory to incorporate novel features of quantum dynamics, stochastics, and measurement
We work within an linear quadratic Gaussian (LQG) framework as in the recent paper of Nurdin, James, and Petersen [19] and utilize numerical optimization together with fundamental analytic results [1] bounding the best possible LQG performance of measurement-based feedback control
With state feedback and in the absence of exogenous noise, such a quadratic cost function would result in a linear quadratic regulator (LQR) optimal control problem [1], but in our optical feedback scenario with Gaussian input fields this becomes a quantum LQG
Summary
As present-day engineering relies broadly and implicitly on real-time feedback control methodology [1], it is difficult to imagine our nascent explorations of quantum engineering advancing to technological relevance without rigorous extensions of core control theory to incorporate novel features of quantum dynamics, stochastics, and measurement. We work within an LQG framework as in the recent paper of Nurdin, James, and Petersen [19] and utilize numerical optimization together with fundamental analytic results [1] bounding the best possible LQG performance of measurement-based feedback control. [14,18,19], we will here refer to measurement-based controllers as “classical” controllers and to coherent feedback controllers as “quantum” controllers This terminology reflects the general distinction that the signal processing required to determine LQG-optimal control actions from a real-time measurement signal can be implemented by a classical electric circuit, while all of the hardware in a coherent feedback loop must be physically describable using quantum mechanics (typically with weak damping)
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