Out-of-plane nonlinear optical responses of superconducting cuprates detected by Terahertz pump-Terahertz probe spectroscopy

We systemically investigated the out-of-plane transient responses of high-temperature superconductor La$_{1.905}$Ba$_{0.095}$CuO$_4$ by THz pump-THz probe spectroscopy. Our experiments present that there are explicit long-lasting temporal oscillations in the pump-probe decay procedure after THz excitations in the superconducting state, which result from the THz nonlinear electrodynamics and Josephson plasmon mode (JPM) along $c$-axis of the crystal. We also elaborated the dissimilarities of the oscillatory signals induced by single-cycle broad-band THz pump pulses and multi-cycle narrow-band ones. For broad-band THz pump, the oscillation central frequency scales linearly with the energy detected by THz probe beam, rather than centering at an individual frequency. That linear dependent relationship has not been observed before. In contrast, the narrow-band THz pump centering at $\omega_{\rm pump}$ turns to consistently drive JPM like alternating electric field, which leads to an 2$\omega_{\rm pump}$ oscillation once $\omega_{\rm pump}$ approaching the energy scale of JPM. By comparing the resonant condition, we further confirm the invisibility of Higgs mode in the out-of-plane transient responses.