## 2 Experiments and Results
While this potentially hints towards a complete quench of the short-range correlations, both spectra are still distinguishable and, thus, a transient state different from the room-temperature phase is observed. Figure 3a shows the maximum quench of the LHB spectral signature as a function of incident pump fluence, as extracted from the LHB dynamics (Figure 3b), where we analyzed the minimum value of the LHB intensity that can be found for all delay times. In agreement with [20], we find an almost linear dependence of the intensity loss from incident pump fluence for \(F<400\)\(\upmu\) cm\({}^{-2}\). This indicates a perturbative excitation regime where the LHB intensity directly corresponds to the number of excited quasi-particles or the amount of deposited energy. For higher \(F\), the observed quench saturates and a maximum suppression of approximately 25 percent is found, resulting in the finite spectral weight that corresponds to the one found in the room-temperature phase as mentioned above. We will discuss these two major findings, (i) a high intensity loss of the LHB signature and (ii) the saturation of this intensity loss as a function of incident fluence, in the following in more detail. In a simplified picture, the 13 Ta 5\(d\) valence electrons of each polaron cluster form sub-bands, where the uppermost half-filled band stemming from the 13 th excess electron is prone to the Mott-Hubbard transition. A loss in LHB intensity reflects either a depopulation of the corresponding electronic band or transient changes in the electronic density of states caused by the suppression of on-site electron-electron interaction [30]. The rather high intensity loss of the LHB signature is likely incompatible with a simple depopulation scheme because it would imply that a majority of the valence electrons are excited, a situation that potentially destabilizes the crystal. Furthermore, no comparable intensity losses are observed in other energetic regions accessible in the experiment. We rather interpret the LHB spectral signature intensity as a direct measure of the strength of short-range electron  
Figure 3: (**a**) Maximum collapse of the LHB peak intensity as a function of incident pump fluence, as extracted from the transient LHB intensity (**b**). The solid black line in (**a**) shows the result of the model calculation (see text) and the corresponding quench of short-range correlation \(S\). The vertical dashed line indicates the fluence at which deviations from a linear dependence are found and the LHB collapse starts to saturate; (**b**) Time dependence of the LHB signature for two selected excitation fluences (\(F=1200\)\(\upmu\)) cm\({}^{-2}\) and \(F=64\)\(\upmu\) cm\({}^{-2}\)). Solid lines are exponential fits used to extract the LHB recovery times (inset in (**b**)), neglecting the oscillatory part of the signal. The resulting error bars are shown in the inset. Please note that the saturation level at higher delays is below the value obtained before pumping (indicated by the dashed horizontal line). correlation \(S\) in the system that can be understood as an \"order parameter\" for the charge ordered state, which is also reflected in temperature-dependent equilibrium photoemission data [12]. We therefore conclude that the saturation of this loss reflects the complete collapse of the short-range interaction responsible for the emergence of the Mott gap and the LHB signature. In accordance with the nanoscale coexistence of insulating and metallic domains (Figure 1), we discuss the transient quench of electronic correlations in a real-space picture. First we note that the geometrical cluster density \(n_{0}=7\times 10^{13}\) cm\({}^{-2}\)[31] is somewhat smaller than the number of incident pump photons \(\frac{F}{\hbar\omega_{1}}\approx 1.6\times 10^{15}\) cm\({}^{-2}\) for \(F=400\)\(\upmu\)J cm\({}^{-2}\) at the approximate saturation threshold, which implies that the excitation of all polaron clusters is in principle possible.