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Recently developed terahertz (THz) two-dimensional coherent spectroscopy(2DCS) is a powerful technique to obtain materials information in a fashionqualitatively different from other spectroscopies. Here, we utilized THz 2DCSto investigate the THz nonlinear response of conventional superconductor NbN.Using broad-band THz pulses as light sources, we observed a third-ordernonlinear signal whose spectral components are peaked at twice thesuperconducting gap energy $2\Delta$. With narrow-band THz pulses, a THznonlinear signal was identified at the driving frequency $\Omega$ and exhibiteda resonant enhancement at temperature when $\Omega = 2\Delta$. Generaltheoretical considerations show that such a resonance can only arise from adisorder-activated paramagnetic coupling between the light and the electroniccurrent. This proves that the nonlinear THz response can access processesdistinct from the diamagnetic Raman-like density fluctuations, which arebelieved to dominate the nonlinear response at optical frequencies in metals.Our numerical simulations reveal that even for a small amount of disorder, the$\Omega=2\Delta$ resonance is dominated by the superconducting amplitude modeover the entire investigated disorder range. This is in contrast to otherresonances, whose amplitude-mode contribution depends on disorder. Our findingsdemonstrate the unique ability of THz 2DCS to explore collective excitationsinaccessible in other spectroscopies.

Revealing novel aspects of light-matter coupling in terahertz  two-dimensional coherent spectroscopy: the case of the amplitude mode in  superconductors