# Non-equilibrium Optical Conductivity: General Theory and Application to Transient Phases

## TL;DR

This paper develops a non-equilibrium theory for optical conductivity in superconductors and charge density waves, revealing how transient states can be characterized and distinguished using shaped light pulses.

## Contribution

It introduces a general non-equilibrium framework for optical conductivity and proposes methods to measure instantaneous superfluid stiffness in transient phases.

## Key findings

- Characteristic time signatures differentiate superconducting, normal, and charge density wave states.
- Single-frequency optical conductivity is hard to interpret outside adiabatic limit.
- Shaping probe light fields can directly measure superfluid stiffness.

## 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.