Trajectory tracking for non-Markovian quantum systems

TL;DR

This paper introduces a systematic reverse engineering scheme to control quantum states in non-Markovian systems, enabling finite-time state transfer and population inversion without engineering decay rates.

Contribution

The authors develop a novel control scheme for non-Markovian quantum systems that does not require engineering decay rates and can achieve arbitrary state trajectories.

Findings

Successfully applied to a driven two-level system

Achieved instantaneous-steady-state tracking

Realized complete population inversion

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