Quantum Robust Stability of a Small Josephson Junction in a Resonant Cavity

This paper applies recent results on the robust stability of nonlinear quantum systems to the case of a Josephson junction in a resonant cavity. The Josephson junction is characterized by a Hamiltonian operator which contains a non-quadratic term involving a cosine function. This leads to a sector bounded nonlinearity which enables the previously developed theory to be applied to this system in order to analyze its stability.Comment: A version of this paper appeared in the proceedings of the 2012 IEEE Multi-conference on Systems and Contro

Quantum Popov robust stability analysis of an optical cavity containing a saturated Kerr medium

This paper applies results on the robust stability of nonlinear quantum systems to a system consisting an optical cavity containing a saturated Kerr medium. The system is characterized by a Hamiltonian operator which contains a non-quadratic term involving a quartic function of the annihilation and creation operators. A saturated version of the Kerr nonlinearity leads to a sector bounded nonlinearity which enables a quantum small gain theorem to be applied to this system in order to analyze its stability. Also, a non-quadratic version of a quantum Popov stability criterion is presented and applied to analyze the stability of this system.Comment: A shortened version will appear in the Proceedings of the 2013 European Control Conferenc

A Direct Coupling Coherent Quantum Observer for a Single Qubit Finite Level Quantum System

This paper considers the problem of constructing a direct coupling quantum observer for a single qubit finite level quantum system plant. The proposed observer is a single mode linear quantum system which is shown to be able to estimate one of the plant variables in a time averaged sense. A numerical example and simulations are included to illustrate the properties of the observer.Comment: A preliminary version of this paper has been accepted to appear in the 2014 Australian Control Conferenc

Coherent-Classical Estimation for Quantum Linear Systems

This paper introduces a problem of coherent-classical estimation for a class of linear quantum systems. In this problem, the estimator is a mixed quantum-classical system which produces a classical estimate of a system variable. The coherent-classical estimator may also involve coherent feedback. An example involving optical squeezers is given to illustrate the efficacy of this idea.Comment: A version of this paper will appear in the Proceedings of the 2013 Australian Control Conferenc