Nonequilibrium optical conductivity: General theory and application to transient phases

Abstract

A non-equilibrium theory of optical conductivity of dirty-limit superconductors and commensurate charge density wave is presented. We discuss the current response to different experimentally relevant light-field probe pulses and show that a single frequency definition of the optical conductivity $\sigma(\omega)\equiv j(\omega)/E(\omega)$ is difficult to interpret out of the adiabatic limit. We identify characteristic time domain signatures distinguishing between superconducting, normal metal and charge density wave states. We also suggest a route to directly address the instantaneous superfluid stiffness of a superconductor by shaping the probe light field.