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Coherent Feedback Control of Linear Quantum Optical Systems with Squeezing Components

Bo Huang, Guofeng Zhang, Lee H.W. Joseph

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The purpose of this paper is to study coherent feedback control of a class of linear quantum systems with squeezing components arising frequently in quantum optics. The H∞ quantum control studied in [1] and quantum LQG control studied in [2] are extende

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Physical Review Applied•Oct 10, 2024•7 citations
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 into the issue of the physical realizability of such quantum systems. The problem of coherent quantum linear quadratic Gaussian (LQG) feedback control studied in H. I. Nurdin, M. R. James, and I. R. Petersen, Automatica, IFAC, 45 (2009), pp. 1837--1846; G. Zhang and M. R. James, IEEE Trans. Automat. Control, 56 (2011), pp. 1535--1550 is reinvestigated in depth. First, the optimization methods in these papers are extended to a multistep optimization algorithm which utilizes ideal squeezers. Second, 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 closed-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.
This paper studies feedback quantum control of a class of linear quantum optical systems by means of squeezing and phase modulation. A new quadrature representation of such systems is introduced, which includes explicitly phase modulation of light fields involved. Some fundamental relations are derived in terms of the new quadrature representation. The coherent quantum LQG control studied in is re-investigated base on controller parametrization and a two-stage optimization approach. Examples are given to illustrate the effectiveness of the results in the paper.
Coherent feedback H∞H^\inftyH∞ control of quantum linear systems
The purpose of this paper is to investigate the coherent feedback H∞H^\inftyH∞ control problem for linear quantum systems. A key contribution is a simplified design methodology that guarantees closed-loop stability and a prescribed level of disturbance attenuation. It is shown that for general linear quantum systems, a physically realizable quantum controller can be obtained by solving at most four Lyapunov equations. In the passive case, a necessary and sufficient condition is provided in terms of two uncoupled pairs of Lyapunov equations. These results represent a significant simplification over the standard approach, which requires solving two coupled algebraic Riccati equations. The effectiveness of the proposed method is demonstrated through two typical quantum optical devices: an empty optical cavity and a degenerate parametric amplifier. These results provide a computationally efficient procedure for the robust and optimal control of quantum optical and optomechanical systems.
Quantum control theory is a rapidly evolving research field, which has developed over the last three decades. Quantum optics has practical importance in quantum technology and provides a promising means of implementing quantum information and computing device. \nIn quantum control, it is difficult to acquire information about quantum states without destroying them since microscopic quantum systems have many unique characteristics such as entanglement and coherence which do not occur in classical mechanical system. Therefore, \nthe Lyapunov-based control methodology is used to first construct an artificial closed-loop controller and then an open-loop law is derived by simulation of the artificial closed-loop system. \n \nThis work considers the stabilization of laser cavity as the main integral part of quantum optical systems through squeezing the output beam of the cavity. As a comprehensive example of this type of system, quantum optomechanical sensors are investigated. To this end, a nonlinear model \nof quantum optomechanical sensors is first extended incorporating various noises. Then, linear quadratic Gaussian (LQG) control method is used to tackle the problem of mode-squeezing in optomechanical sensors. \nCoherent feedback quantum control is synthesized by incorporating both shot noise and back-action noise to attenuate the output noise well below the shot noise level (Two waves are said to be coherent if they have a constant relative phase). In the second phase of this work, due to entanglement of the system with critical uncertainties and technical limitations such as laser noise and detector imprecision, robust H [infinity] method is employed for the robust stabilization and robust performance of the system in practice. In H [infinity] methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this. The effectiveness of the proposed control strategy in squeezing the cavity output beam is demonstrated by simulation.
The noise reduction in squeezed states makes them a powerful nonclassical resource in quantum technologies, especially in quantum sensing, and an essential step for the ongoing development of non-Gaussian states. In particular, optical and mechanical squeezing can both be generated when light interacts with a mechanical oscillator. Here we use a linear optical system as a controller and use coherent optical feedback to enhance squeezing in the unresolved-sideband regime of optomechanics. Feedback control is generally profitable for cooling, manipulating, and stabilizing the dynamics of mechanical oscillators; coherent feedback is then notable for its ability to steer a quantum system toward the highest squeezing without measurement, avoiding backaction. We thoroughly maximize optical and conditional mechanical squeezing feasible with state-of-the-art experimental setups and derive the optimal conditions under which quantum squeezing is generated in the system. Published by the American Physical Society 2024