Coherent Feedback Control of Linear Quantum Optical Systems via Squeezing and Phase Shift

TL;DR

This paper presents a theoretical and numerical analysis of using squeezing and phase shifts in coherent feedback control for linear quantum optical systems, introducing a new quadrature representation and optimization methods.

Contribution

It introduces a quadrature representation with phase shifters, extends optimization methods for quantum LQG control, and proposes a two-stage optimization approach with improved control performance.

Findings

Numerical results show improved LQG control performance with the new approach.

A sufficient condition for stability when replacing ideal squeezers with realistic amplifiers.

Performance convergence discussed in the context of realistic quantum components.

Abstract

The purpose of this paper is to present a theoretic and numerical study of utilizing squeezing and phase shift in coherent feedback control of linear quantum optical systems. A quadrature representation with built-in phase shifters is proposed for such systems. Fundamental structural characterizations of linear quantum optical systems are derived in terms of the new quadrature representation. These results reveal considerable insights of issue of physical realizability of such quantum systems. The problem of coherent quantum LQG feedback control studied in [35,50] is re-investigated in depth. Firstly, the optimization methods in [35,50] are extended to a multi-step optimization algorithm which utilizes ideal squeezers. Secondly, a two-stage optimization approach is proposed on the basis of controller parametrization. Numerical studies show that closed-loop systems designed via the second approach may offer LQG control performance even better than that when the closed-loop systems are in the vacuum state. When ideal squeezers in a close-loop system are replaced by (more realistic) degenerate parametric amplifiers, a sufficient condition is derived for the asymptotic stability of the resultant new closed-loop system; the issue of performance convergence is also discussed in the LQG control setting.