Comment on arXiv:2210.01114: Optical Saturation Produces Spurious Evidence for Photoinduced Superconductivity in K$_3$C$_{60}$

In the manuscript arXiv:2210.01114, Dodge and co-authors discuss the influence of pump-probe profile deformations on the reconstructed non-equilibrium optical conductivity of K$_3$C$_{60}$. They state that when pump-induced saturation of the probe response is taken into account, the reconstructed optical properties are not superconducting-like, as was claimed in a number of experimental reports by our group. We show here that the conclusion reached by Dodge et al. is unjustified. In fact, independent of the specific model, including the problematic saturation profile proposed by the authors, the reconstructed optical properties are those of a finite temperature superconductor. The true fingerprint of superconductivity, which is the $1/\omega$ divergence of the imaginary conductivity, $\sigma_{2}(\omega)$, is retained and is virtually independent of the chosen model. The only model-dependent feature is the degree of gapping in $\sigma_{1}(\omega)$. In all cases the extracted optical properties reflect the presence of residual quasiparticles, which at finite temperatures are inevitably present alongside the superfluid.
Comment: 3 pages, 1 figure, comment on arXiv:2210.01114