2021/08/04 by Eugenio Pozzoli, Pozzoli, Eugenio
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Laser-Matter Interactions and Applications #Mathematical Physics (math-ph) #Quantum optics and atomic interactions #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2108.01943
23 pages, 6 figures
openalex publication_date 2021/08/04 · arxiv created 2021/09/30 · arxiv updated 2021/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study both the classical and quantum rotational dynamics of an asymmetric top molecule, controlled through three orthogonal electric fields that interact with its dipole moment. The main difficulties in studying the controllability of these infinite-dimensional quantum systems are the presence of severe spectral degeneracies in the drift Hamiltonian and the nonsolvability of the stationary free Schrödinger equation, which lead us to apply a perturbative Lie algebraic approach. In this paper we show that, while the classical equations given by the Hamiltonian system on \rm SO(3)× ℝ3 are controllable for all values of the rotational constants and all dipole configurations, the Schödinger equation for the quantum evolution on L2(\rm SO(3)) is approximately controllable for almost all values of the rotational constants if and only if the dipole is not parallel to any of the principal axes of inertia of the asymmetric rigid body.