A Sufficient Condition for Partial Ensemble Controllability of Bilinear Schr\"odinger Equations with Bounded Coupling Terms

TL;DR

This paper establishes a sufficient condition for the partial controllability of infinite-dimensional bilinear quantum systems, using geometric and averaging control methods, demonstrated through molecular rotation examples.

Contribution

It introduces a new sufficient condition for partial ensemble controllability of bilinear Schrödinger equations with bounded coupling, extending control theory in quantum systems.

Findings

Condition verified for specific quantum systems

Control techniques adapted from finite to infinite dimensions

Illustrated with molecular rotation example

Abstract

This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging control techniques applied on finite dimensional approximation of the infinite dimensional system. The results are illustrated with the planar rotation of a linear molecule.