Clocking the Onset of Bilayer Coherence in a High-${\mathrm{T}}_{\mathrm{C}}$ Cuprate

In cuprates, a precursor state of superconductivity is speculated to exist above the critical temperature ${\mathrm{T}}_{\mathrm{C}}$. Here we show via a combination of far-infrared ellipsometry and ultrafast broadband optical spectroscopy that signatures of such a state can be obtained via three independent observables in an underdoped sample of NdBa${}_2$Cu${}_3$O${}_{6+\delta }$. The pseudogap correlations were disentangled from the response of laser-broken pairs by clocking their characteristic time-scales. The onset of a superconducting precursor state was found at a temperature ${\mathrm{T}}_{\mathrm{O}\mathrm{N}\mathrm{S}}$ $>$ ${\mathrm{T}}_{\mathrm{C}}$, consistent with the temperature scale identified via static optical spectroscopy. Furthermore, the temperature evolution of the coherent vibration of the Ba ion, strongly renormalized by the onset of superconductivity, revealed a pronounced anomaly at the same temperature ${\mathrm{T}}_{\mathrm{O}\mathrm{N}\mathrm{S}}$. The microscopic nature of such a precursor state is discussed in terms of pre-formed pairs and enhanced bilayer coherence.