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

In cuprates, a precursor state of superconductivity is speculated to exist above the critical temperature $\mathrm{T_C}$. 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 $\mathrm{T_{ONS}}$ $>$ $\mathrm{T_C}$, 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 $\mathrm{T_{ONS}}$. The microscopic nature of such a precursor state is discussed in terms of pre-formed pairs and enhanced bilayer coherence.