Transient Higgs oscillations and high-order nonlinear light-Higgs coupling in a terahertz wave driven NbN superconductor

We study the nonlinear optical response in a superconducting NbN thin film with a strong terahertz (THz) wave. In. addition to the expected third-harmonic generation, we observe a transient oscillation which softens in frequency with temperature increasing towards the superconducting transition temperature T-c. We identify this feature as transient Higgs oscillation. To verify this proposal, we introduce a time-frequency resolved technique, a spectrogram for visualizing the THz spectrum. The dynamic decaying behavior of the oscillation is observed, which is consistent with the theoretical expectation of intrinsic Higgs oscillation. Moreover, we observe a higher-order nonlinear optics effect, i.e., fifth-harmonic generation, which we assign to the higher-order coupling between the Higgs mode and electromagnetic field.