Optimal control theory for rapid-adiabatic passage techniques in inhomogeneous external fields

TL;DR

This paper applies optimal control theory to quantum rapid-adiabatic passage in inhomogeneous fields, analyzing non-adiabatic effects, geometric phases, and path topologies to improve control robustness.

Contribution

It introduces a non-adiabatic correction to Bloch dynamics and links geometric phases with control path topologies in SCRAP.

Findings

Optimal control fields are robust against inhomogeneous electric fields.

Non-zero geometric phases occur for certain adiabatic paths.

Different cost functionals influence the topology of control parameter paths.

Abstract

The present paper reports on results of quantum dynamics calculations for Stark-chirp rapid-adiabatic passage (SCRAP) in two-level systems with electric fields computed with the optimal control theory. The Pontryagin maximum principle is used to determine the robust optimal control fields in the presence of time-varying and spatially-inhomogeneous perturbing electric fields. The concept of a non-adiabatic correction to the Bloch vector dynamics is introduced and discussed. The existence of a non-zero geometric phase is proved for certain adiabatic paths, which correspond to the complete population return in the rapid-adiabatic passage. A connection is shown between the geometric phase and a measure of the non-adiabatic effects in the time evolution of the state vector during SCRAP. Different cost functionals used in the optimal control scheme are shown to correlate with different topologies of the paths followed by the parameters of the Hamiltonian, which tightly relates to the values of the geometric phase acquired by the adiabatic wavefunction.