Finite-time Landau-Zener processes and counter-diabatic driving in open systems: beyond Born, Markov and Rotating-wave approximations

TL;DR

This study explores finite-time Landau-Zener processes in open quantum systems, employing a hierarchy equation method to analyze fidelity without common approximations, and investigates counter-diabatic driving and dynamical decoupling effects.

Contribution

It provides a numerically exact analysis of Landau-Zener processes beyond typical approximations, revealing the complex interplay of system-bath coupling, driving protocols, and environment effects.

Findings

Fidelity shows non-monotonic dependence on coupling and sweep rate.

Counter-diabatic driving improves fidelity only for short processes.

Dynamical decoupling can mitigate decoherence while preserving counter-diabatic benefits.

Abstract

We investigate Landau-Zener processes modeled by a two-level quantum system, with its finite bias energy varied in time and in the presence of a single broadened cavity mode at zero temperature. By applying the hierarchy equation method to the Landau-Zener problem, we computationally study the survival fidelity of adiabatic states without Born, Markov, rotating-wave or other perturbative approximations. With this treatment it also becomes possible to investigate cases with very strong system-bath coupling. Different from a previous study of infinite-time Landau-Zener processes, the fidelity of the time-evolving state as compared with instantaneous adiabatic states shows non-monotonic dependence on the system-bath coupling and on the sweep rate of the bias. We then consider the effect of applying a counter-diabatic driving field, which is found to be useful in improving the fidelity only for sufficiently short Landau-Zener processes. Numerically exact results show that different counter-diabatic driving fields can have much different robustness against environment effects. Lastly, using a case study we discuss the possibility of introducing a dynamical decoupling field in order to eliminate the decoherence effect of the environment and at the same time to retain the positive role of a counter-diabatic field. Our work indicates that finite-time Landau-Zener processes with counter-diabatic driving offer a fruitful test bed to understand controlled adiabatic processes in open systems.