On Exponential Stabilization of Spin $-\frac{1}{2}$ Systems

In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound of the convergence rate. Based on stochastic Lyapunov techniques, we propose a parametrized feedback controller ensuring exponential convergence toward the target state. Moreover, we provide a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appearing in the controller in the convergence rate. Finally, we illustrate the efficiency of such feedback controller through simulations.