We theoretically investigate coherent optical excitations of collective modes in two-band BCS superconductors, which accommodate two Higgs modes and one Leggett mode corresponding, respectively, to the amplitude and relative-phase oscillations of the superconducting order parameters associated with the two bands. We find, based on a mean-field analysis, that each collective mode can be resonantly excited through a nonlinear light-matter coupling when the doubled frequency of the driving field coincides with the frequency of the corresponding mode. Among the two Higgs modes, the higher-energy one exhibits a sharp resonance with light, while the lower-energy mode has a broadened resonance width. The Leggett mode is found to be resonantly induced by a homogeneous ac electric field because the leading nonlinear effect generates a potential offset between the two bands that couples to the relative phase of the order parameters. The resonance for the Leggett mode becomes sharper with increasing temperature. All of these light-induced collective modes along with density fluctuations contribute to the third-harmonic generation. We also predict an experimental possibility of optical detection of the Leggett mode.

In multiband superconductors, multiple collective modes exist associated with the multiple order parameters. Oscillations of the amplitude and the relative phase of the order parameters are called Higgs and Leggett modes, respectively. Recently, it has been suggested that nonmagnetic impurity scattering would enhance nonlinear coupling between the Higgs mode and an electromagnetic wave with a frequency located in the superconducting gap region, while its effect on the Leggett mode is still unresolved. Here, we theoretically investigated the nonlinear optical response of multiband Bardeen-Cooper-Schrieffer-type superconductors in the presence of nonmagnetic impurities with a density matrix approach extending the Mattis-Bardeen model of linear response. We found that the drastic enhancement of nonlinear optical response due to the nonmagnetic impurity scattering occurs only for the Higgs modes and not for the Leggett mode. As a result, both the light-induced dynamics of the superconducting gaps and the resulting third-harmonic generation are dominated by the Higgs modes. We also examined the role of quasiparticle excitations to find that they give the subdominant contribution to the third-harmonic generation.

Higgs mode in superconductors, i.e. the collective amplitude mode of the order parameter does not associate with charge nor spin fluctuations, therefore it does not couple to the electromagnetic field in the linear response regime. On the contrary to this common understanding, here, we demonstrate that, if the dc supercurrent is introduced into the superconductor, the Higgs mode becomes infrared active and is directly observed in the linear optical conductivity measurement. We observed a sharp resonant peak at ω = 2∆ in the optical conductivity spectrum of a thin-film NbN in the presence of dc supercurrent, showing a reasonable agreement with the recent theoretical prediction. The method as proven by this work opens a new pathway to study the Higgs mode in a wide variety of superconductors.

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We investigated the interaction between an intense terahertz (THz) pulse and excitons in bulk GaAs by using THz pump near-infrared (NIR) optical probe spectroscopy. We observed a clear spectral oscillation in the NIR transient absorption spectra at low temperature, which is interpreted as the THz pump-induced perturbed free induction decay (PFID) of the excitonic interband polarization. We performed a numerical simulation based on a microscopic theory and identified that the observed PFID signal originates from the THz field-induced ionization of excitons. Using a real-space representation of the excitonic wave function, we visualized how the ionization of an exciton proceeds under the intense single-cycle THz electric field. We also calculated the nonlinear susceptibility with the lowest-order perturbation theory assuming a weak THz pump, which showed a similar spectral feature with that obtained by the full treatment to field-induced ionization process. This coincidence is attributed to the fact that 1s-excitonic interband polarization is modified predominantly through interactions with the p-wave component of the excitonic wave function. A simple phenomenological expression of the PFID signal is presented to discuss effects of the THz pump pulse duration on the spectral oscillation.