Designing adiabatic time-evolution from high frequency bichromatic sources

TL;DR

This paper explores how bichromatic fields with different frequency regimes can be engineered to produce controlled adiabatic quantum evolutions in a two-level system, including cases where traditional approximations fail.

Contribution

It introduces a non-perturbative analysis of bichromatic driving, demonstrating methods to achieve adiabatic evolution using high frequencies and multi-photon resonances.

Findings

Two large frequencies can generate effective adiabatic evolution.

High frequency corrections enable tunable adiabatic control over the Bloch sphere.

Resonances can dominate dynamics when one frequency is large and the other small.

Abstract

We investigate the quantum dynamics of a two-level system driven by a bichromatic field, using a non-perturbative analysis. We make special emphasis in the case of two large frequencies, where the Magnus expansion can fail, and in the case of a large and a small frequency, where resonances can dominate. In the first case, we show that two large frequencies can be combined to produce an effective adiabatic evolution. In the second case, we show that high frequency terms (which naturally arise as corrections to the adiabatic evolution obtained in the first case) can be used to produce a highly tunable adiabatic evolution over the whole Bloch sphere, controlled by multi-photon resonances.