Figure 4. Energy-resolved spectra and differential fit in the superconducting phase.

(a) The δR/R(ω,t) at t=400 fs, that is, the delay at which the maximum signal is measured, is shown for three different dopings in the superconducting phase (T=20 K). The black solid lines are differential fits to the data obtained assuming a modification of the 1.5 and 2 eV interband transitions. The values of the fitting parameters for the optimally doped sample (OP96) are reported in the Supplementary Table S2. The inset displays the relative variation of the optical conductivity for the three dopings, obtained from the data. The scale of the horizontal axis is the same as in the main panel. (b) The spectral weight variation, δSW_tot=δSW_{1.5 eV}+δSW_{2 eV}=δω²_p(1.5)/8+δω²_p(2)/8 (ω_p(1.5) and ω_p(2) being the plasma frequencies of the interband Lorentz oscillators at 1.5 and 2 eV), is reported at different delays for the three dopings. The maximum value of δSW_tot corresponds to the minimum Δ_SC value at ∼400 fs, that is, after a partial electron-boson thermalization. The error bars represent the standard deviation obtained from the fit. (c) The δSW_tot value, relative to the extrapolated zero-temperature value, is estimated from single-colour measurements and reported as a function of the temperature for OP96. Similar results are obtained for UD83 and OD86. (d) The dynamics of the superconducting gap, assuming the proportionality between δR/R(ω,t) and the photoexcited quasiparticle density21,22, is reported (Supplementary Note 4). At a pump fluence of 10 μJ cm⁻², the maximum gap decrease is ∼20% at 400 fs delay time. (e), The black circles represent the maximum δSW_tot=δSW_{1.5 eV}+δSW_{2 eV}, observed at 400 fs, as a function of the doping level. The error bars take into account the stability of the differential fit on the equilibrium dielectric function (Supplementary Notes 1,2). The left axis has the same units as panel b. The T_c–p phase diagram is reported on the right-top axes.