Dynamical Symmetry Breaking in Floquet Systems: Application to High Harmonic Generation

Floquet systems often exhibit dynamical symmetries (DS) that govern the time-dependent dynamics
and result in selection rules. When the DS is broken by a perturbation, deviations from these
selection rules are expected. While these deviations are often used for exploring the perturbations
and perturbed dynamics, so far, they are not described by a general theory. In my talk, I
will consider dynamical symmetry breaking in Floquet systems from a general perspective,
formulating a general theory that analytically connects the symmetry-broken and fully-symmetric
systems. Using a symmetry breaking laser field as a model perturbation, I will begin by explicitly
showing that the broken symmetry induces ‘selection rules’ for the allowed/forbidden contributions
to selection rule deviations. We will identify that these ‘selection rules’ are a manifestation of an
unexplored class of DS in what at first glance appear to be symmetry broken systems but are in fact
systems that exhibit dynamical symmetries in a high-dimensional synthetic space. Lastly, we will
compare predictions obtained from the analytical theory to numerical calculations and experimental
measurements of DS breaking in HHG. To conclude, I will discuss how the approach can be applied
to other types of symmetry breaking due to intrinsic properties of the medium, or properties of the
light-matter dressed system .