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

Abstract

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 broad-band THz pulses as light sources, we observed a third-order nonlinear signal whose spectral components are peaked at twice the superconducting gap energy $2\Delta$. With narrow-band THz pulses, a THz nonlinear signal was identified at the driving frequency $\Omega$ and exhibited a resonant enhancement at temperature when $\Omega =2\Delta$. General theoretical considerations show that such a resonance can only arise 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 $\Omega =2\Delta$ 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.

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• Discovery of an Unconventional Quantum Echo by Interference of Higgs Coherence
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• Direct observation of the Higgs particle in a superconductor by non-equilibrium Raman scattering
• Amplitude mode in a multi-gap superconductor MgB${}_2$ investigated by terahertz two-dimensional coherent spectroscopy
• Disentangling spin excitation continua in classical and quantum magnets using 2D nonlinear spectroscopy
• Extracting Nonlinear Dynamical Response Functions from Time Evolution
• Spatially-resolved dynamics of the amplitude Schmid-Higgs mode in disordered superconductors
• Anomalous electronic energy relaxation and soft phonons in the Dirac semimetal Cd${}_3$As${}_2$
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• Spatially resolved collective modes in d-wave superconductors
• Unifying Measurement Schemes in 2-D Terahertz Spectroscopy
• Two-dimensional coherent spectroscopy of disordered superconductors in the narrow-band and broad-band limits
• Optical conductivity of a dirty current-carrying superconductor
• Resonant second harmonic generation in a two-dimensional electron system
• Momentum-resolved two-dimensional spectroscopy as a probe of nonlinear quantum field dynamics
• Measuring intrinsic relaxation rates in superconductors using nonlinear response
• Higgs and Nambu-Goldstone modes in a spin-1 $XY$ model with long-range interactions
• Third-harmonic generation in superconductors: Role of quantum geometry in the competition between Higgs mode and quasiparticles
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
• Two-dimensional THz spectroscopy in electronic systems: a many-body diagrammatic approach