Periodic control laws for bilinear quantum systems with discrete spectrum

TL;DR

This paper develops bounds on the error of finite-dimensional approximations of bilinear quantum systems and uses averaging methods to establish controllability, demonstrated on a 2D rotating molecule model.

Contribution

It introduces error bounds for Galerkin approximations of infinite-dimensional bilinear Schrödinger equations and applies averaging techniques for controllability analysis.

Findings

Error bounds for Galerkin approximations established

Controllability results obtained via averaging methods

Application demonstrated on a 2D rotating molecule model

Abstract

We provide bounds on the error between dynamics of an infinite dimensional bilinear Schr\"odinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations to obtain constructive controllability results. As an illustration, the methods are applied on a model of a 2D rotating molecule.