ROBUST FEEDBACK STABILIZATION OF N-LEVEL QUANTUM SPIN SYSTEMS

In this paper, we consider N-level quantum angular momentum systems interacting with electromagnetic fields undergoing quantum nondemolition measurements in continuous-time. We suppose unawareness of the initial state and physical parameters, entailing the introduction of an additional state representing the estimated quantum state. The evolution of the quantum state and its estimation is described by a coupled stochastic master equation. Here, we study the asymptotic behavior of such a system in the presence of a feedback controller. We provide sufficient conditions on the feedback controller and on the estimated parameters that guarantee exponential stabilization of the coupled stochastic system toward an eigenstate of the measurement operator. Furthermore, we estimate the corresponding rate of convergence. We also provide parametrized feedback laws satisfying such conditions. Our results show the robustness of the feedback stabilization strategy considered in [W. Liang, N. H. Amini, and P. Mason, SIAM J. Control Optim., 57 (2019), pp. 3939-3960] in the case of imprecise initialization of the estimated state and with respect to the unknown physical parameters.

Automated summary

This paper explores the asymptotic behavior of N-level quantum angular momentum systems interacting with electromagnetic fields undergoing quantum nondemolition measurements, and examines the conditions for achieving exponential stabilization through a feedback controller. The results demonstrate the robustness of the feedback stabilization strategy in cases of imprecise initialization of the estimated state and unknown physical parameters.