Engineering adiabaticity at an avoided crossing with optimal control

TL;DR

This paper explores optimizing adiabatic and diabatic transitions in the Landau-Zener model using non-uniform sweeps and optimal control, enabling precise manipulation of quantum state populations within limited timeframes.

Contribution

It introduces a pulse design combining linear and oscillating components to control diabaticity and extends optimal control methods to preserve adiabaticity efficiently.

Findings

Oscillating pulses induce population jumps modeled by photon-assisted Landau-Zener transitions.

Optimal control methods can maintain adiabaticity with limited evolution time.

A non-uniform quantum speed limit is identified for adiabatic processes.

Abstract

We investigate ways to optimize adiabaticity and diabaticity in the Landau-Zener model with non-uniform sweeps. We show how diabaticity can be engineered with a pulse consisting of a linear sweep augmented by an oscillating term. We show that the oscillation leads to jumps in populations whose value can be accurately modeled using a model of multiple, photon-assisted Landau-Zener transitions, which generalizes work by Wubs et al. [New J. Phys. 7, 218 (2005)]. We extend the study on diabaticity using methods derived from optimal control. We also show how to preserve adiabaticity with optimal pulses at limited time, finding a non-uniform quantum speed limit.