In this paper, an open-loop control is applied to stabilize a two-level quantum particle by an external optical field. To achieve this goal, the speed gradient method is implemented. The efficiency of this method is shown by numerical experiments.
The methods of mathematical control theory are widely used in the modern physics, but still they are less popular in quantum science. We will discuss the aspects of control theory, which are the most useful in applications to the real problems of quantum optics. We apply this technique to control the behavior of the two-level quantum particles (atoms) in the modulated external optical field in the frame of the so called "semi classical model", where quantum two-level atomic system (all other levels are neglected) interacts with classical electromagnetic field. In this paper we propose a simple model of feedforward (open-loop) control for the quantum particle system, which is a basement for further investigation of two-level quantum particle in the external one-dimensional optical field.
We discuss the model of a quantum bit driven by an external classical field without decay in the rotating wave approximation. In such a model, the whole evolution of the qubit states takes place on the Bloch sphere. We reformulate the model as a unitless set of real ordinary differential equations and use the normalized external field as a feedback control parameter. The closed-loop algorithm is designed in the form of the speed gradient, driving the dynamical system towards minimizing a given nonnegative goal function expressed via the qubit variables. We investigate the achievability of the control goal, and focus on the most important features of the speed gradient algorithm applied to a quantum system in comparison with classical systems. Our approach is valid for the control over the ground and excited population levels, and over the qubit phase variables. The paper was presented at PhysCon2024.
The paper proposes a gradient method for feedback control and stabilization of quantum systems using Schröodinger’s and Lindblad’s descriptions. The eigenstates of the quantum system are defined by the spin model. First, a gradient-based control law is computed using Schröodinger’s description. Next, an estimate of state of the quantum system is obtained using Lindblad’s differential equation. In the latter case, by applying Lyapunov’s stability theory and LaSalle’s invariance principle one can compute a gradient control law which assures that the quantum system’s state will track the desirable state within acceptable accuracy levels. The performance of the control loop is studied through simulation experiments for the case of a two-qubit quantum system.