Effect of feedback on the control of a two-level dissipative quantum system

TL;DR

This paper demonstrates how feedback control can modify the stationary state and influence time-optimal control in a two-level dissipative quantum system, using geometric control theory and the Lindblad master equation.

Contribution

It introduces a feedback control approach to alter stationary states and analyzes its impact on time-optimal control in dissipative quantum systems.

Findings

Feedback control modifies stationary states.

Feedback influences time-optimal control trajectories.

Analysis based on geometric control theory and Lindblad equation.

Abstract

We show that it is possible to modify the stationary state by a feedback control in a two-level dissipative quantum system. Based on the geometric control theory, we also analyze the effect of the feedback on the time-optimal control in the dissipative system governed by the Lindblad master equation. These effects are reflected in the function $\Delta_A(\vec{x})$ and $\Delta_B(\vec{x})$ that characterize the optimal trajectories, as well as the switching function $\Phi(t)$ and $\theta(t),$ which characterize the switching point in time for the time-optimal trajectory.