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European Control Conference (ECC)

Designing quantum networks of feedback control systems of optical QED cavity in interacting Fock space

B. C. Roy, Pradip Das

Published Aug 1, 2009• 0 citations
Publisher

Abstract

This paper is concerned with the state space modelling of closed optical QED feedback control system in interacting Fock space which is shown to be a generalization of Langevin stochastic model in boson Fock space. This work includes the design of quantum networks of the feedback systems of QED cavity using two-mode beam splitter device at the input to the cavity and a single mode fractional beam splitter device at the output of the cavity in interacting mode and their stability analysis using Nyquist criterion.

DOI
10.23919/ecc.2009.7074400

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This paper is concerned with the state space modelling of closed optical QED feedback control system in interacting Fock space which is shown to be a generalization of Langevin stochastic model in boson Fock space. This work includes the design of quantum networks of the feedback systems of QED cavity using two-mode beam splitter device at the input to the cavity and a single mode fractional beam splitter device at the output of the cavity in interacting mode and their stability analysis using Nyquist criterion.
The present article is concerned with the study of quantum electrodynamics (QED) in interacting Fock space and a generalised approach of modelling quantum feedback systems of the optical QED cavities. The dynamical behaviour and the state space representation in stochastic field of the optical QED system provide the basis for developing quantum feedback QED control system. This study is also motivated by the design of quantum networks of any number of optical QED baths connected in parallel. Nyquist stability of the feedback control system in the interacting Fock space using two-mode beam splitter device at the input and a single-mode fractional beam splitter device at the output of the cavity has been analysed. The degree of stability of the quantum feedback control system of the cavity QED is studied by measuring gain margin and phase margin of the system in terms of parameters of the beam splitter.
This paper is concerned with the analysis of linear quantum optical networks. It provides a systematic approach to the construction a model for a given quantum network in terms of a system of quantum stochastic differential equations. This corresponds to a classical state space model. The linear quantum optical networks under consideration consist of interconnections between optical cavities, optical squeezers, and beamsplitters. These models can then be used in the design of quantum feedback control systems for these networks.
This paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators. A quantum optical closed-loop, including a plant and controller, is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view, in order to facilitate the use of control theory in microscopic world described by quantum theory. In particular, an input-output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed. This would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics. This paper is divided into two parts. The first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device, cavity, that can be regarded as a unit of quantum dynamics of bosonic modes. The formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations. The input-output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems. In the follow-up paper, the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory, uncertainty principle, e.g., and some applications are presented.
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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.