Trajectory tracking for non-Markovian quantum systems

Abstract

We propose a systematic scheme to engineer quantum states of a quantum system governed by a time-convolutionless non-Markovian master equation. According to the idea of the reverse engineering, the general algebraic equation to determine the control parameters, such as coherent and incoherent control fields, are presented. Without artificially engineering the time-dependent decay rates and persisting the environment-induced Lamb shifts, the quantum state can still be transferred into the target state with a finite period of time along an arbitrary designed trajectory in Hilbert space strictly. As an application, we apply our scheme to a driven two-level non-Markovian system, and realize the instantaneous steady state tracking and the complete population inversion with control parameters which are available in experimental-settings.