The use of intense and phase-stable THz laser pulses to coherently probe collective excitations can occur via excitation pathways which defy the typical resonant driving operative for the linear response. Here we show that in superconductors the nonlinear optical response can be enhanced when excited quasiparticles activate a (non-resonant) static displacement of the superconducting order parameter, in full analogy with the displacive excitation of coherent phonons in opaque materials. By combining numerical simulations with analytical results we demonstrate that the displacive Higgs mechanism is operative in both s-wave and d-wave superconductors, and we show that its relaxation at large times is connected to energy-dissipative processes [1]. The theoretical results are compared with measurements of the phase of the nonlinear first harmonic in superconducting s-wave NbN [2] and of the energy relaxation time measured via pump-probe protocols. Our results offer a novel perspective on the ability of THz spectroscopy at intense fields to measure, and eventually control, the parametric dependence of the optical response on collective degrees of freedom.

This work has been supported by the EU under project MORE-TEM ERC-SYN (grant agreement No 951215) and by Italian MIUR under project PRIN2022-CoInEx (2022WS9MS4).

[1] Jacopo Fiore, Irene Zanotti, Kota Katsumi, N. Peter Armitage, Goetz Seibold, Claudio Castellani and Lara Benfatto, preprint 2026

[2 ]Kota Katsumi, Jacopo Fiore, Mattia Udina, Ralph Romero III, David Darbalas, John Jesudasa, Pratap Raychaudhuri, Goetz Seibold, Lara Benfatto, N.P. Armitage, Phys. Rev. Lett. 132, 256903 (2024)