TY - GEN A1 - Katsumi, Kota A1 - Fiore, Jacopo A1 - Udina, Mattia A1 - Romero, Ralph A1 - Barbalas, David A1 - Jesudasan, John A1 - Raychaudhuri, Pratap A1 - Seibold, Götz A1 - Benfatto, Lara A1 - Armitage, N. P. T1 - Revealing novel aspects of light-matter coupling by Terahertz Two-Dimensional Coherent Spectroscopy: the case of the amplitude mode in superconductors T2 - Physical Review Letters N2 - Recently developed terahertz (THz) two-dimensional coherent spectroscopy (2DCS) is a powerful technique to obtain materials information in a fashion qualitatively different from other spectroscopies. Here, we utilized THz 2DCS to investigate the THz nonlinear response of conventional superconductor NbN. Using broadband THz pulses as light sources, we observed a third-order nonlinear signal whose spectral components are peaked at twice the superconducting gap energy 2⁢Δ. With narrow-band THz pulses, a THz nonlinear signal was identified at the driving frequency Ω and exhibited a resonant enhancement at temperature when Ω=2⁢Δ. General theoretical considerations show that such a resonance can arise only from a disorder-activated paramagnetic coupling between the light and the electronic current. This proves that the nonlinear THz response can access processes distinct from the diamagnetic Raman-like density fluctuations, which are believed to dominate the nonlinear response at optical frequencies in metals. Our numerical simulations reveal that, even for a small amount of disorder, the Ω=2⁢Δ resonance is dominated by the superconducting amplitude mode over the entire investigated disorder range. This is in contrast to other resonances, whose amplitude-mode contribution depends on disorder. Our findings demonstrate the unique ability of THz 2DCS to explore collective excitations inaccessible in other spectroscopies. Y1 - 2024 UR - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.256903 U6 - https://doi.org/10.1103/PhysRevLett.132.256903 VL - 132 ER -