Necessary and sufficient condition for quantum adiabatic evolution by unitary control fields

TL;DR

This paper derives a precise condition for quantum adiabatic evolution using unitary control fields, revealing how eigenenergies and degeneracies can change rapidly while eigenstates vary slowly, and shows fast modulation can reduce errors.

Contribution

It provides a necessary and sufficient condition for adiabatic evolution with geometric phases and analyzes the impact of control field modulation on nonadiabatic errors.

Findings

Exact nonadiabatic correction derived

Condition for adiabatic evolution with geometric phases established

Fast modulation fields can reduce nonadiabatic errors

Abstract

We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic evolution with geometric phases is provided and we determine that in the adiabatic evolution, while the eigenstates are slowly varying, the eigenenergies and degeneracy of the Hamiltonian can change rapidly. We exemplify this result by the example of the adiabatic evolution driven by parametrized pulse sequences. For driving fields that are rotating slowly with the same average energy and evolution path, fast modulation fields can have smaller nonadiabatic errors than obtained under the traditional approach with a constant amplitude.