Periodic excitations of bilinear quantum systems

TL;DR

This paper extends the classical Rotating Wave Approximation, used for finite-dimensional quantum systems, to infinite-dimensional systems, providing rigorous theoretical justification and explicit convergence estimates for periodic control laws.

Contribution

It generalizes the Rotating Wave Approximation to infinite-dimensional quantum systems with explicit convergence bounds.

Findings

The classical averaging theory applies to finite-dimensional systems.

The paper provides explicit convergence estimates for the approximation.

Extension of the RWA to infinite-dimensional systems is validated.

Abstract

A well-known method of transferring the population of a quantum system from an eigenspace of the free Hamiltonian to another is to use a periodic control law with an angular frequency equal to the difference of the eigenvalues. For finite dimensional quantum systems, the classical theory of averaging provides a rigorous explanation of this experimentally validated result. This paper extends this finite dimensional result, known as the Rotating Wave Approximation, to infinite dimensional systems and provides explicit convergence estimates.