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International Journal of Control

Modelling of quantum networks of feedback QED systems in interacting Fock space

B.C. Roy, Pradip Das

Published Aug 14, 2009• 7 citations
Publisher

Abstract

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.

DOI
10.1080/00207170903015164

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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.
Quantum Coherent Feedback Control of an NNN-Level Atom With Multiple Excitations
The purpose of this article is to study the dynamics of a quantum coherent feedback network, where anNNN-level atom is coupled with a cavity and the cavity is also coupled with a single or multiple parallel waveguides. When the atom is initialized at the highest energy level, it can emit multiple photons into the cavity, and the photons can be further transmitted to the waveguides and reinteract with the cavity quantum electrodynamics (cavity-QED) system. The transmission of photons in the waveguide can construct a feedback channel with a delay determined by the length of the waveguide. We model the dynamics of the atomic and photonic states of the cavity-QED system as a linear control system with delay. By tuning the control parameters such as the coupling strengths among the atom, cavity and waveguide, the eigenstates of the quantum system can be exponentially stable or unstable, and the exponential stability of the linear quantum control system with delay is related with the generation of single- and multiphoton states. Besides, when the cavity-QED system is coupled with multiple parallel waveguides, the emitted photons oscillate among different waveguides and the stability of quantum states is influenced by the feedback loop length and coupling strengths among waveguides.
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.
The purpose of this article is to study two-photon dynamics induced by the coherent feedback control of a cavity quantum electrodynamics (cavity-QED) system coupled to a waveguide. In this setup, the two-level system in the cavity can work as a photon source, and the photon emitted into the waveguide can reinteract with the cavity-QED system many times after the transmission and reflection in the waveguide, during which the feedback can tune the number of the photons in and out of the cavity. We analyze the dynamics of two-photon processes in this coherent feedback network in two scenarios: the continuous mode coupling scheme and the discrete periodic mode coupling scheme between the waveguide and cavity. The difference of these coupling schemes is due to their relative scales and the number of semitransparent mirrors for coupling. Specifically, in the continuous mode coupling scheme, the generation of two-photon states is influenced by the length of the feedback loop by the waveguide and the coupling strength between the waveguide and the cavity-QED system. By tuning the length of the waveguide and the coupling strength, we are able to generate two-photon states efficiently. In the discrete periodic mode coupling scheme, the Rabi oscillation in the cavity can be stabilized and there are no notable two-photon states in the waveguide.