Light-matter interaction in quantum materials is one of the critical aspects that elucidates their
intriguing properties. In particular, the terahertz (THz) frequency range is of great interest as it
allows us to access rich low-energy excitations in such materials. Recent advancements in
generating an intense THz pulse enabled the investigations of nonlinear light-matter interaction,
which can provide information unreachable by the linear light-matter coupling. More recently, THz
2D coherent spectroscopy (THz 2DCS) has emerged as a new technique to disentangle different
nonlinear optical processes of magnons, phonons, and plasmons. Yet, understanding the THz
2DCS spectra is still in its infancy.
In this talk, I will present the recent results of THz 2DCS in the case of a conventional
superconductor NbN to elucidate the light-matter interaction of the amplitude collective excitation
of the superconducting order parameter, which is often referred to as the Higgs mode [1]. Using
broad-band THz pulses as light sources, we observed a third-order nonlinear optical response
whose power spectrum peaked at twice the superconducting gap energy 2∆. With narrow-band
THz pulses, a THz nonlinear signal was identified at the driving frequency Ω and displayed a
resonant enhancement at temperature when Ω = 2∆. General theoretical considerations show
that such resonance can only stem from a disorder-activated paramagnetic light-matter interaction.
Numerical simulations demonstrate that even for a small amount of disorder, the Ω = 2∆
resonance is dominated by the superconducting amplitude mode. We further investigated the THz
2DCS response in the case of MgB2, a multigap counterpart of NbN [2]. I will discuss the essential
difference in THz nonlinear responses between MgB2 and NbN. These studies demonstrated the
ability of THz 2DCS to explore the physics of the amplitude mode in superconductors, which
would open a new door to studying collective excitations in other types of unconventional
superconductors.

[1] K. Katsumi, J. Fiore, M. Udina, R. Romero III, D. Barbalas, J. Jesudasan, P. Raychaudhuri, G. Seibold,
L. Benfatto, and N. P. Armitage, Phys. Rev. Lett. 132, 256903 (2024).
[2] K. Katsumi, J. Liang, R. Romero III, K. Chen, X. Xi, and N. P. Armitage,