Sum rules for light-dressed matter

Abstract: Light-driven matter can exhibit qualitatively distinct electronic and optical properties from those observed at equilibrium. We introduce generalized sum rules for the optical properties of driven systems by both quantum and classical light. For classical light, it shows that the sum of all Fourier components, indexed by n, of the time-dependent dipole matrix elements between dressed states weighted by the corresponding quasienergy difference in the first Floquet Brillouin zone plus n driving frequency is a constant, determined by the number of electrons. An analogous sum rule for quantum light-dressing is also derived. These developments provide guidance for the control of effective optical properties of matter by light fields.