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Superconducting (SC) fluctuations in cuprate superconductors have beenextensively studied to gain a deep insight into preformed Cooper pairs abovethe SC transition temperature $T_{\text{c}}$. While the various measurements,such as the terahertz (THz) optical conductivity, Nernst effect, angle-resolvedphotoemission spectroscopy (ARPES), and scanning tunneling microscopy (STM)measurements have provided the signature of the SC fluctuations, the onsettemperature of the SC fluctuations depends on the measurement scheme. Here, weshed light on the Higgs mode to investigate the SC fluctuations, as it is thedirect fingerprint of SC order parameter and can help elucidate the developmentof SC phase coherence. We perform THz pump-optical probe spectroscopy forunderdoped and overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212) thin films. Theoscillatory behavior in the pump-probe signal (THz Kerr signal) observed in theSC phase has been identified as the Higgs mode in single crystals in ourprevious work [K. Katsumi et al., Phys. Rev. Lett. 120, 117001 (2018)], but twoonset temperatures are identified above $T_{\text{c}}$. Combined with theresults of the single crystals in a wide range of doping, we find that thefirst onset $T_1^{\text{ons}}$ is 10-30 K above $T_{\text{c}}$.$T_1^{\text{ons}}$ coincides with that of the superfluid density $N_s$extracted from the THz optical conductivity. Hence, $T_1^{\text{ons}}$ isinterpreted as the onset of macroscopic SC phase stiffness. On the other hand,the second onset $T_2^{\text{ons}}$ is identified at substantially higher than$T_{\text{c}}$, whose origin is discussed in terms of preformed Cooper pairs.

Superconducting fluctuations probed by the Higgs mode in Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ thin films