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Proceedings of the ... American Control Conference/Proceedings of the American Control Conference

Squeezing enhancement of degenerate parametric amplifiers via coherent feedback control

Chuanxin Bian, Guofeng Zhang, Joseph H. W. Lee

Published Jun 1, 2012• 0 citations
Publisher

Abstract

The purpose of this paper is to present an efficient coherent feedback control technique for squeezing enhancement of degenerate parametric amplifiers (DPAs). The feedback controllers to be designed are in the form of linear quantum stochastic systems which can be described by quantum feedback network theory recently developed. The problem of squeezing enhancement is formulated as a non-convex constrained nonlinear programming problem. Compared with previous study, the proposed approach reveals clear advantage when DPAs are lossy, as is always the case in practice.

DOI
10.1109/acc.2012.6314987

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The purpose of this paper is to present an efficient coherent feedback control technique for squeezing enhancement of degenerate parametric amplifiers (DPAs). The feedback controllers to be designed are in the form of linear quantum stochastic systems which can be described by quantum feedback network theory recently developed. The problem of squeezing enhancement is formulated as a non-convex constrained nonlinear programming problem. Compared with previous study, the proposed approach reveals clear advantage when DPAs are lossy, as is always the case in practice.
The purpose of this article is to present an efficient coherent feedback control technique for squeezing enhancement of degenerate parametric amplifiers (DPAs). The feedback controllers to be designed are in the form of linear quantum stochastic systems which can be described by quantum feedback networks theory recently developed. The problem of squeezing enhancement is formulated as a non-convex constrained nonlinear programming problem, whose solution yields the coherent feedback controllers to be designed. Compared with the previous study, the proposed approach reveals clear advantage when DPAs are lossy, as is always the case in practice. Based on the recently developed quantum network synthesis theory, we show how the designed coherent feedback controllers can be implemented by means of quantum optical devices.
The theory of quantum feedback networks has recently been developed with the aim of showing how quantum input-output components may be connected together so as to control, stabilize, or enhance the performance of one of the subcomponents. In this paper, we show how the degree to which an idealized component (a degenerate parametric amplifier in the strong-coupling regime) can squeeze input fields may be enhanced by placing the component in loop in a simple feedback mechanism involving a beam splitter. We study the spectral properties of output fields, placing particular emphasis on the elastic and inelastic components of the power density.
The squeezing level of light on atomic resonance produced by a degenerate optical parametric amplifier (DOPA) is now limited by blue or violet pump-light-induced loss, and it is difficult to improve the squeezing by simply reducing the loss of DOPA. In this study, two promising schemes, namely, the cascaded DOPA (C-DOPA) and the coherent feedback-controlled DOPA (CFC-DOPA), are theoretically discussed. For a ideal case, the CFC-DOPA can realize infinite squeezing output but requires almost infinite accuracy in phase locking. For a practical case with feasible physical parameters of realistic systems, the performance of squeezing enhancement for the C-DOPA and CFC-DOPA is compared. The C-DOPA shows advantages in the megahertz frequency range, while the CFC-DOPA shows advantages in the low-frequency range. At a general analysis frequency of 2 MHz, C-DOPA shows better robustness against the loss of the system. As a price, it requires a smaller instability tolerance for phase locking. With the C-DOPA, the squeezing on Rb atomic resonance can be pushed from − 5 d B to − 7 d B . Our analytical results can provide a valuable reference for designing experimental devices to efficiently produce high-quality squeezed light on atomic resonance, which has potential applications in quantum information processing and quantum metrology.
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.