Controllability of the bilinear Schr\"odinger equation with several controls and application to a 3D molecule

TL;DR

This paper demonstrates the approximate rotational controllability of a polar linear molecule using three laser fields, based on a general controllability result for the bilinear Schrödinger equation with multiple controls.

Contribution

It extends controllability results to the bilinear Schrödinger equation with several controls and applies this to control a 3D molecule with laser fields.

Findings

Achieved approximate rotational controllability of a polar molecule.

Established a general controllability result for bilinear Schrödinger equations with multiple controls.

Applied the theoretical results to a practical molecular control scenario.

Abstract

We show the approximate rotational controllability of a polar linear molecule by means of three nonresonant linear polarized laser fields. The result is based on a general approximate controllability result for the bilinear Schr\"odinger equation, with wavefunction varying in the unit sphere of an infinite-dimensional Hilbert space and with several control potentials, under the assumption that the internal Hamiltonian has discrete spectrum.