Non-linear optical effects and third-harmonic generation in superconductors: Cooper-pairs vs Higgs mode contribution

TL;DR

This paper investigates non-linear optical effects in superconductors, demonstrating that Cooper-pair excitations dominate third-harmonic generation, with Higgs mode contributions being smaller unless specific experimental conditions are used.

Contribution

It reveals that third-harmonic generation in superconductors is primarily driven by Cooper-pair excitations, contrasting with the Higgs mode, and suggests experimental setups to enhance Higgs contributions.

Findings

Cooper-pair excitations dominate third-harmonic generation.

Higgs mode contributions are generally smaller.

Proper polarization and symmetry can enhance Higgs mode detection.

Abstract

The recent observation of a transmitted Thz pulse oscillating at three times the frequency of the incident light paves the way to a new protocol to access resonant excitations in a superconductor. Here we show that this non-linear optical process is dominated by light-induced excitation of Cooper pairs, in analogy with a standard Raman experiment. The collective amplitude (Higgs) fluctuations of the superconducting order parameter give in general a smaller contribution, unless one designs the experiment by combining properly the light polarization with the lattice symmetry.