Degree of Time-Reversal and Dynamical Symmetry Breaking in Electromagnetic Fields and Its Connection to Floquet Engineering

Lightwave control of electron dynamics and Floquet dressing in condensed matter has recently been explored with polarization-tailored laser pulses in both theory and experiments. Tailored light offers a unique approach to coherently control various phenomena in solids, from photocurrents to topology and ultrafast quantum processes such as high harmonic generation. By employing multiple carrier waves and their polarizations and phases as degrees of freedom, the extent of symmetry breaking and its impact on out-of-equilibrium phenomena can be manipulated. However, in this emerging field it remains unclear what are the key aspects of electromagnetic excitation that control responses, especially in highly nonlinear regimes. We propose a quantitative measure for the degree of time-reversal symmetry breaking (DTRSB) in a light field, which has long been well-established as an essential component for Floquet topology. We also present generalized measures for the degree of any point-group symmetry breaking in electromagnetic fields that can be employed for analysis of various experimental settings. By numerically testing the Floquet dressing of graphene with bichromatic waves that are individually linearly polarized, we show that the size of the gap opening is correlated to the DTRSB, as well as to the chirality of the electromagnetic field. Our work thus provides a roadmap for analyzing measurements and guiding experiments with tailored light control of Floquet phases and ultrafast electron dynamics.