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Automatica

Cascade cavity realization for a class of complex transfer functions arising in coherent quantum feedback control

Ian R. Petersen

Published Apr 14, 2011• 54 citations
Publisher
DOI
10.1016/j.automatica.2011.03.006

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This paper presents a realization algorithm for a class of complex transfer functions corresponding to physically realizable complex linear quantum systems. The class of complex linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. It is shown that for almost all quantum optical systems within this class, the corresponding transfer function can be realized as a cascade connection involving only cavities and phase-shifters.
The realization of transfer functions of Linear Quantum Stochastic Systems (LQSSs) is an issue of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. In this paper, we review two realization methods proposed by the authors in [1], [2], [3], [4]. The first one uses a cascade of a static linear quantum-optical network and single-mode optical cavities, while the second uses a feedback network of such cavities, along with static linear quantum-optical networks that pre- and post-process the cavity network inputs and outputs.
This paper presents a method for approximating a class of complex transfer function matrices corresponding to physically realizable complex linear quantum systems. The class of complex linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. This approximation method builds on a previous result for the cascade realization of these transfer function matrices and gives good approximations at low frequencies.