We have investigated the terahertz (THz) nonlinear response of the multigap superconductor ${\mathrm{MgB}}_2$, using THz two-dimensional coherent spectroscopy (THz 2DCS). With broadband THz drive fields, we identified a nonlinear response at twice the lower superconducting gap energy $2{\mathrm{\Delta }}_{\pi }$ at the lowest temperatures. Using narrow-band THz driving pulses, we observed first (FH) and third harmonic responses. The FH intensity shows a monotonic increase with decreasing temperature when properly normalized by the driving field strength. This is distinct from the single-gap superconductor NbN, where the FH signal exhibited a resonant enhancement at temperatures when twice the gap energy $2\mathrm{\Delta }$ was resonant with the driving photon energy, which was interpreted to originate from the superconducting amplitude mode. Our results in ${\mathrm{MgB}}_2$ are consistent with a well-defined amplitude mode only at the lowest temperatures and indicate strong damping as temperature increases. This likely indicates the importance of interband coupling in ${\mathrm{MgB}}_2$ and its influence on the nature of the amplitude mode and its damping.

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• Light-matter interaction
• Multiband superconductivity
• Nonlinear optics
• Low-temperature superconductors
• Terahertz spectroscopy
• Two-dimensional coherent spectroscopy