Abstract
Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. Here we formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems, and derive their correspondence to observable selection rules. We apply the theory to harmonic generation, deriving closed-form tables linking DSs of the driving laser and medium (gas, liquid, or solid) in (2+1)D and (3+1)D geometries to the allowed and forbidden harmonic orders and their polarizations. We identify symmetries, including time-reversal-based, reflection-based, and elliptical-based DSs, which lead to selection rules that are not explained by currently known conservation laws. We expect the theory to be useful for ultrafast high harmonic symmetry-breaking spectroscopy, as well as in various other systems such as Floquet topological insulators.
Highlights
Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules
We introduced symmetries that involve time-reversal operations, and an elliptical symmetry that does not exist in molecular groups
We proved that if a given Hamiltonian commutes with a dynamical group the generators of the group constrain the temporal evolution of Floquet states and the associated physical observables
Summary
Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. We systematically derive DSs as generalized products of spatial and temporal transformations in both (2 + 1)D and (3 + 1)D, yielding closed-form dynamical groups that describe the symmetries of Floquet systems.
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