Higgs spectroscopy of superconductors in non-equilibrium

Higgs spectroscopy is a new and emergent field that allows to classify and determine the superconducting order parameter by means of ultra-fast optical spectroscopy. There are two ways to activate the Higgs mode in superconductors, namely a single-cycle 'quench' or an adiabatic, multicycle 'drive' pulse. In the talk I will review and report on the latest progress on both theory and experiments on Higgs spectroscopy, in particular on the role of the third-harmonic-generation (THG) and the possible IR-activation of the Higgs mode by impurities or external dc current. I also provide new predictions for time-resolved ARPES experiments in which, after a quench, a continuum of Higgs mode is observable and a phase information of the superconducting gap function would be possible to extract. Finally, I show that the Higgs mode can maybe solve the 25-years-old A1g-puzzle in equilibrium Raman scattering on high-Tc cuprates.