Helical-photon-dressed states determining unidirectional π-electron rotations in aromatic ring molecules.

We theoretically demonstrated that helical-photon-dressed states determine the rotational directions of the π-electrons of aromatic ring molecules formed by a circularly polarized or an elliptically polarized laser. This theory was verified using a minimal three-electronic-state model under the frozen nuclei condition. The model consists of the ground state and either a doubly degenerate electronic excited state or two quasi-degenerate excited states. Three helical-photon-dressed states were derived by solving the time-dependent Schrödinger equation within the semi-classical treatment of light-molecule interactions and rotating wave approximation. The angular momenta of the two helical-photon-dressed states represent the classical rotational direction, and that of the remaining state represents the opposite rotation, that is, non-classical rotation. Classical rotation means that π-electrons have the same rotational direction as that of a given helical electric field vector and obeys the classical equations of motion. Non-classical rotation indicates that the rotational direction is opposite to that of the helical electric field vector. Non-classical rotation is forbidden in an aromatic ring molecule with high symmetry formed by a circularly polarized laser but is allowed in a low symmetric aromatic ring molecule. The sum of the angular momenta of the three dressed states is zero. This is called the sum law for the angular momentum components in this paper. Benzene (D6h) and toluene (CS) were adopted as typical aromatic ring molecules of high and low symmetries, respectively. Finally, considering the effects of nuclear vibrations in the adiabatic approximation, an expression for the π-electron angular momentum was derived and applied to toluene.