# Higgs Oscillations in time-resolved Optical Conductivity

## TL;DR

This paper calculates the time-resolved optical conductivity of a pumped superconductor using a non-equilibrium approach, revealing Higgs oscillations and order parameter dynamics in the transient state.

## Contribution

It introduces a method to compute full vertex corrected optical conductivity in non-equilibrium superconductors, highlighting Higgs mode oscillations.

## Key findings

- Transient suppression of superconductivity observed.
- Higgs amplitude mode oscillations detected in the spectrum.
- Recovery dynamics of the order parameter characterized.

## Abstract

Driving superconductors out of equilibrium is a promising avenue to study their equilibrium properties as well as to control the superconducting state. Non-equilibrium superconductors are often studied using time resolved optical conductivity measurements. Thus, the characterization of a superconducting state in a pump driven non-equilibrium state requires careful attention in the time domain. We calculate time-resolved optical conductivity of a pumped superconducting state using a non-equilibrium Keldysh approach. Through functional derivation, the optical conductivity is obtained with full vertex corrections and used to characterize the transient superconducting state. The transient optical conductivity shows the suppression of the superconducting order parameter in the time domain. The subsequent recovery of the order parameter exhibits oscillatory behavior that corresponds to the Higgs amplitude mode, and may be seen in several parts of the spectrum.