# Detecting superconductivity out-of-equilibrium

## TL;DR

This paper explores how to reliably detect transient superconductivity out-of-equilibrium, emphasizing the limitations of optical conductivity measurements and proposing time-resolved ARPES as a better probe.

## Contribution

It demonstrates that optical conductivity alone is insufficient for identifying superconductivity out-of-equilibrium and advocates for using time-resolved ARPES to detect condensate formation.

## Key findings

- Optical conductivity evolution is not enough to confirm superconductivity out-of-equilibrium.
- Time-resolved ARPES can effectively probe for condensate formation.
- Current experimental methods may misidentify transient superconducting states.

## Abstract

Recent pump-probe experiments on underdoped cuprates and similar systems suggest the existence of a transient superconducting state above $\mathrm{T}_c$. This poses the question how to reliably identify the emergence of long-range order, in particular superconductivity, out-of-equilibrium. We investigate this point by studying a quantum quench in an extended Hubbard model and by computing various observables, which are used to identify (quasi-)long-range order in equilibrium. Our findings imply that, in contrast to current experimental studies, it does not suffice to study the time evolution of the optical conductivity to identify superconductivity. In turn, we suggest to utilize time-resolved ARPES experiments to probe for the formation of a condensate in the two-particle channel.