Zeno Dynamics for Open Quantum Systems

In this paper we formulate limit Zeno dynamics of general open systems as the adiabatic elimination of fast components. We are able to exploit previous work on adiabatic elimination of quantum stochastic models to give explicitly the conditions under which open Zeno dynamics will exist. The open systems formulation is further developed as a framework for Zeno master equations, and Zeno filtering (that is, quantum trajectories based on a limit Zeno dynamical model). We discuss several models from the point of view of quantum control. For the case of linear quantum stochastic systems we present a condition for stability of the asymptotic Zeno dynamics.Comment: 17 pages, 3 figure

Construction of bilinear control Hamiltonians using the series product and quantum feedback

We show that it is possible to construct closed quantum systems governed by a bilinear Hamiltonian depending on an arbitrary input signal. This is achieved by coupling the system to a quantum input field and performing a feedback of the output field back into the system to cancel out the stochastic effects, with the signal being added to the field between these events and later subtracted. Here we assume the zero time delay limit between the various connections and operations.Comment: 9 pages, 3 figure

Enhancement of field squeezing using coherent feedback

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.Comment: 8 pages, 4 figure

Quantum Dissipative Systems and Feedback Control Design by Interconnection

Abstract—The purpose of this paper is to extend J.C. Willems’ theory of dissipative systems to open quantum systems described by quantum noise models. This theory, which combines ideas from quantum physics and control theory, provides useful meth-ods for analysis and design of dissipative quantum systems. We describe the interaction of the plant and a class of external systems, called exosystems, in terms of feedback networks of interconnected open quantum systems. Our results include an infinitesimal characterization of the dissipation property, which generalizes the well-known Positive Real and Bounded Real Lemmas, and is used to study some properties of quantum dissipative systems. We also show how to formulate control design problems using network models for open quantum systems, which implements Willems ’ “control by interconnection ” for open quantum systems. This control design formulation includes, for example, standard problems of stabilization, regulation, and robust control

The Series Product and Its Application to Quantum Feedforward and Feedback Networks

The purpose of this paper is to present simple and general algebraic methods for describing series connections in quantum networks. These methods build on and generalize existing methods for series (or cascade) connections by allowing for more general interfaces, and by introducing an efficient algebraic tool, the series product. We also introduce another product, which we call the concatenation product, that is useful for assembling and representing systems without necessarily having connections. We show how the concatenation and series products can be used to describe feedforward and feedback networks. A selection of examples from the quantum control literature are analyzed to illustrate the utility of our network modeling methodology.Comment: To appear, IEEE Transactions on Automatic Control, 200