I. R. Petersen

S. Z. Sayed Hassen, M. Heurs, E. H. Huntington et al.

This paper considers the application of integral Linear Quadratic Gaussian (LQG) optimal control theory to a problem of cavity locking in quantum optics. The cavity locking problem involves controlling the error between the laser frequency and the resonant frequency of the cavity. A model for the cavity system, which comprises a piezo-electric actuator and an optical cavity is experimentally determined using a subspace identification method. An LQG controller which includes integral action is synthesized to stabilize the frequency of the cavity to the laser frequency and to reject low frequency noise. The controller is successfully implemented in the laboratory using a dSpace DSP board.

H. I. Nurdin, I. R. Petersen, M. R. James

This paper uses a system theoretic approach to show that classical linear time invariant controllers cannot generate steady state entanglement in a bipartite Gaussian quantum system which is initialized in a Gaussian state. The paper also shows that the use of classical linear controllers cannot generate entanglement in a finite time from a bipartite system initialized in a separable Gaussian state. The approach reveals connections between system theoretic concepts and the well known physical principle that local operations and classical communications cannot generate entangled states starting from separable states.

Luis A. Duffaut Espinosa, Z. Miao, I. R. Petersen et al.

The goal of this paper is to provide conditions under which a quantum stochastic differential equation (QSDE) preserves the commutation and anticommutation relations of the SU(n) algebra, and thus describes the evolution of an open n-level quantum system. One of the challenges in the approach lies in the handling of the so-called anomaly coefficients of SU(n). Then, it is shown that the physical realizability conditions recently developed by the authors for open n-level quantum systems also imply preservation of commutation and anticommutation relations.

A. J. Shaiju, I. R. Petersen, M. R. James

In this paper, we formulate and solve a guaranteed cost control problem for a class of uncertain linear stochastic quantum systems. For these quantum systems, a connection with an associated classical (non-quantum) system is first established. Using this connection, the desired guaranteed cost results are established. The theory presented is illustrated using an example from quantum optics.

H. I. Nurdin, S. Grivopoulos, I. R. Petersen

This paper establishes that generic linear quantum stochastic systems have a pure cascade realization of their transfer function, generalizing an earlier result established only for the special class of completely passive linear quantum stochastic systems. In particular, a cascade realization therefore exists for generic active linear quantum stochastic systems that require an external source of quanta to operate. The results facilitate a simplified realization of generic linear quantum stochastic systems for applications such as coherent feedback control and optical filtering. The key tools that are developed are algorithms for symplectic QR and Schur decompositions. It is shown that generic real square matrices of even dimension can be transformed into a lower $2 \times 2$ block triangular form by a symplectic similarity transformation. The linear algebraic results herein may be of independent interest for applications beyond the problem of transfer function realization for quantum systems. Numerical examples are included to illustrate the main results. In particular, one example describes an equivalent realization of the transfer function of a nondegenerate parametric amplifier as the cascade interconnection of two degenerate parametric amplifiers with an additional outcoupling mirror.