Magnus expansion for a chirped quantum two-level system

TL;DR

This paper develops a Magnus expansion approach for a chirped quantum two-level system, providing a time-independent effective Hamiltonian and higher-order corrections, applicable to complex many-body systems.

Contribution

It introduces a novel Magnus expansion method for chirped quantum systems, extending to many-body cases and including higher-order corrections.

Findings

Derived a time-independent effective Hamiltonian for chirped systems

Matched lowest order dynamics with rotating wave approximation

Included higher-order corrections related to Bloch-Siegert shifts

Abstract

We derive a Magnus expansion for a frequency chirped quantum two-level system. We obtain a time-independent effective Hamiltonian which generates a stroboscopic time evolution. At lowest order the according dynamics is identical to results from using a rotating wave approximation. We determine, furthermore, also the next higher order corrections within our expansion scheme in correspondence to the Bloch-Siegert shifts for harmonically driven systems. Importantly, our scheme can be extended to more complicated systems, i.e. even many-body systems.