Controllability of the bilinear Schrödinger equation with several controls and application to a 3D molecule

Ugo Boscain (1, 2) , Marco Caponigro (3, 4) , Mario Sigalotti (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 GECO - Geometric Control Design
3 CCIB - Center for Computational and Integrative Biology [Camden]
4 Department of Mathematical Sciences [Camden]

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 Schrödinger 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.

Domains: Optimization and Control [math.OC]

Ugo Boscain, Marco Caponigro, Mario Sigalotti. Controllability of the bilinear Schrödinger equation with several controls and application to a 3D molecule. 2012 IEEE 51st Annual Conference on Decision and Control (CDC), Dec 2012, Maui, HI, United States. pp.3038-3043, ⟨10.1109/CDC.2012.6426289⟩. ⟨hal-00691706⟩