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2019

Classical and quantum controllability of a rotating symmetric molecule

Boscain, Ugo, Pozzoli, Eugenio, Sigalotti, Mario

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In this paper we study the controllability problem for a symmetric-top molecule, both for its classical and quantum rotational dynamics.

The molecule is controlled through three orthogonal electric fields interacting with its electric dipole.
We characterize the controllability in terms of the dipole position: when it lies along the symmetry axis of the molecule neither the classical nor the quantum dynamics are controllable, due to the presence of a conserved quantity, the third component of the total angular momentum; when it lies in the orthogonal plane to the symmetry axis, a quantum symmetry arises, due to the superposition of symmetric states, which has no classical counterpart.
If the dipole is neither along the symmetry axis nor orthogonal to it, controllability for the classical dynamics and approximate controllability for the quantum dynamics are proved to hold.

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