Coherent controllers for optical-feedback cooling of quantum oscillators

TL;DR

This paper demonstrates that coherent optical-feedback controllers can outperform measurement-based feedback in cooling quantum oscillators, leveraging quantum stochastic control theory and numerical optimization.

Contribution

It introduces a framework for analyzing and optimizing coherent feedback schemes for quantum resonators, showing their advantages over traditional measurement-based methods.

Findings

Coherent controllers outperform measurement-based feedback in low excitation regimes.

Embedding resonators in interferometers enables all-optical feedback with improved cooling performance.

Numerical optimization confirms the superiority of coherent control schemes in quantum regimes.

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.