Superadiabatic driving of a three-level quantum system

TL;DR

This paper explores superadiabatic control of a three-level quantum system with multiple avoided crossings, analyzing the effectiveness of treating the control as independent two-level problems and assessing fidelity in realistic scenarios.

Contribution

It demonstrates that separate two-level Landau-Zener models can approximate control of complex three-level systems despite algebraic decay of control peaks.

Findings

Control peaks decay algebraically over time

Separate two-level models can approximate three-level control

Fidelity depends on intercrossing separation

Abstract

We study superadiabatic quantum control of a three-level quantum system whose energy spectrum exhibits multiple avoided crossings. In particular, we investigate the possibility of treating the full control task in terms of independent two-level Landau-Zener problems. We first show that the time profiles of the elements of the full control Hamiltonian are characterized by peaks centered around the crossing times. These peaks decay algebraically for large times. In principle, such a power-law scaling invalidates the hypothesis of perfect separability. Nonetheless, we address the problem from a pragmatic point of view by studying the fidelity obtained through separate control as a function of the intercrossing separation. This procedure may be a good approach to achieve approximate adiabatic driving of a specific instantaneous eigenstate in realistic implementations.