Signatures of three-dimensional photo-induced superconductivity in YBa$_2$Cu$_3$O$_{6.48}$

Resonant optical excitation of apical-oxygen phonon modes in underdoped YBa$_2$Cu$_3$O$_{6+x}$ has been shown to induce superconducting-like optical properties at temperatures far higher than the equilibrium $T_C$. All of the evidence collected so far has been based on the changes of the THz frequency $c$-axis response. In these measurements, the capacitive interlayer coupling was seen to transform into an inductive response, reminiscent of a superconducting state, an assignement that was strengthened by recent measurements of ultrafast magnetic field expulsion. Here, we report the first experimental determination of the transient in-plane optical properties. These experiements have so far been challenging because of the high in-plane equilibrium reflectivity, from which small changes in the optical response determine the transient conductivity. We observe a photo-induced in-plane optical gap $2\Delta\simeq30$ cm$^{-1}$ and a divergent imaginary conductivity, also consistent with photo-induced superconductivity. A global fit to these data suggests that in- and out-of-plane electronic properties never completely equilibrate during the dynamics.