## 2 Experiments and Results
Under the assumption of a linear response to the pump laser pulse, where every absorbed photon can excite a single cluster site once, the excited cluster density \(n_{x}\) as a function of incident pump fluence \(F\) can be described by a simple differential equation of the form  
\[\frac{dn_{x}}{dF}=\frac{\gamma}{\hbar\omega_{1}}\left(\frac{n_{0}-n_{x}}{n_{0} }\right)\,, \tag{1}\]  
where \(\gamma=(1-R)(1-e^{-c/\lambda})\) is the pump photon absorption probability within the probed sample depth \(c\), which we assume to be the first sample layer (\(c\) = 0.596 nm [31]). \(R\) = 0.49 and \(\lambda\) = 70 nm are the optical reflectivity and penetration depth for \(\hbar\omega_{1}\) = 1.55 eV, respectively [21; 32]. Assuming a linear relation between the number of excited clusters and the LHB intensity, the intensity collapse is given by \(C=n_{x}/n_{0}\). As mentioned before, the saturation of the LHB intensity loss results in a finite spectral weight in the corresponding energy window which is comparable to the one found in the room-temperature phase. Correspondingly, the correlation strength \(S\) might be defined as \(S\) = 1 in the unperturbed state and \(S\) = 0 in the case where the LHB intensity is completely lost and the 25 percent reduction in intensity is observed (\(S\propto(1-C)\)). The solution of Equation (1) is shown as a solid line in Figure 3a. Despite the simplicity of the model and the underlying assumptions, both, the almost linear dependence for \(F\) < 400 \(\upmu\)J cm\({}^{-2}\) and the saturating behavior for \(F\) > 400 \(\upmu\)J cm\({}^{-2}\) can be reproduced without further rescaling. For high excitation fluences (\(F\) > 1000 \(\upmu\)J cm\({}^{-2}\)), an almost complete reduction of short-range correlation is observed. As mentioned before the excitation fluences under which an almost complete quench occurs are close to those for switching the material into the hidden phase. Based on the above discussions, we will now turn towards the re-equilibration of the system, which is reflected by the recovery of LHB intensity (Figure 3b). The recovery of the LHB intensity is shown in Figure 3b for two different pump fluences. The recovery times \(\tau_{LHB}\) (inset in Figure 3b) are extracted from the transients of the LHB intensity by fitting with an exponential function that was convoluted with a Gaussian resolution function (solid lines in Figure 3b). For low excitation densities (\(F\) < 400 \(\upmu\)J cm\({}^{-2}\)), the recovery times slightly decrease as function of \(F\) from 1 ps to 900 fs with a minimum occurring at the excitation level where the saturation of the LHB intensity quench sets in. For higher fluences, the recovery time increases up to a maximum value of 1.2 ps, which corresponds to a few oscillation cycles of the CDW amplitude mode (\(T_{CDW}\) = 400 fs). In general, these timescales are significantly longer than the carrier hopping time \(t=\hbar/W\approx 14\) fs [13; 19] or the characteristic electron-phonon energy transfer time of \(\tau_{e-ph}\approx\) 200-350 fs reported in literature [20; 33]. This difference in time scales raises the question on the nature of the complete recovery of the Mott state, which we address here. As on the sub-picosecond timescale a majority of the electronic excess energy is already transferred to the lattice system via incoherent excitation of phonons, it is reasonable to first discuss the scenario of an almost thermalized, heated lattice during the recovery of charge order. Assuming that the total excess energy provided by the pump pulse is transferred to the lattice system, we calculated a final lattice temperature of 104 K for \(F\) = 1500 \(\upmu\)J/cm\({}^{2}\) and sample base temperature of 80 K, respectively [34]. Since the recovery time of the LHB signature is only weakly and non-monotonously dependent of excitation fluence, a simple thermally activated process can clearly be excluded.