Dynamical symmetries of time-periodic Hamiltonians

Abstract

The interaction of atoms, molecules, crystals, and nanotubes with time-periodic laser fields can lead to high-order dynamical symmetries (DS's). Here we employ group theoretical methods to study the DS-related properties (quantum numbers, nonaccidental degeneracies) of quantum systems possessing high-order DS's. As explicit examples we take finite-order rotation symmetry in point and plane groups, and a circularly polarized laser field. We find that nonaccidental degeneracies induced by spatial and time-reversal symmetries may not be lifted inside the laser field. A general result of this work is that the time-evolution operator needs to be computed only up to $1/N$ [or, even, $1/(2N)]$ of the optical cycle, where N is the order of the DS. This allows a substantial reduction of the computational effort required for studying the time-dependent dynamics of such systems.