## 3 Discussion
The final, quasi-equilibrated state after a few ps is different from the initial state as evident from partial recovery of LHB intensity (Figure 3b) and characterized by an decreased amplitude of the CDW lattice distortion [35] that persists up to the time scale of 10 ps, where the CDW amplitude mode phonon is largely damped out due to anharmonic coupling. (iv) Full re-equilibration of the system due to heat transfer out of the excited sample volume on nano- to microsecond time scales occurs, resulting in a reduction of excited clusters within the probed sample volume [28]. This process leads to a re-establishment of the initial (mesoscopic) state before excitation, unless the system has been switched into a meta-stable, hidden state [25] due to sufficiently strong excitation. Of particular interest here is the dynamic pathway between the initial state after excitation (i) and the final state achieved after few ps (iii), as it is discussed in the context of the formation of the hidden state [25; 26; 27] and domain wall dynamics [28]. Based on the localized excitation scheme and our experimental findings we propose the following scenario:  
The quasi-equilibrated state (iii) after photo-excitation must be characterized by specific real-space arrangements of the excited clusters, as randomly distributed defects tend to aggregate to form domain walls which can effectively lower the free energy of the system [45]. Correspondingly the equilibration of the initial excited state (i) requires hopping of the excited polarons. Due to the weak and non-monotonous dependence of the LHB recovery time on excitation fluence (Figure 3b), we exclude thermally activated processes to be responsible for this spatial rearrangement. Readopting the equilibrium pictures of CDW/Mott-formation in 1\(T\)-TaS\({}_{2}\) (Figure 1), we expect that the contraction of individual polaron clusters leads to the formation of localization centers of the charge density. Accordingly, inter-star charge transfer caused by de-localization of the ground state carriers requires expansion of the clusters and, thus, a nuclear configuration that is facilitated by the population of the CDW amplitude mode phonon which remains populated on the 10 ps time scale (Figure 4a). This transfer of excitation should not be confused with the significantly faster hopping of carriers in the Mott ground state [13], since it also requires a transfer of the lattice excitation which leads to an effective reduction of the systems free energy. Finally, full equilibration of the system occurs on timescales of a few oscillation periods, which allows for the formation of the final real-space configuration. This sequence is sketched in Figure 5.  
The real-space picture discussed here is compatible with all experimental findings. The formation of the correlated electronic ground state is inherently linked to the periodic lattice distortion, which is reflected by the saturating behavior of both corresponding signatures (Figures 3a and 4b). The optical quench of charge order coherently excites the associated optical phonon modes, which--on the other hand--facilitates charge transfer processes between individual clusters. On long time scales, the system is left behind with a finite amount of deposited energy which leads to an increase in electronic and lattice temperature, reflecting either a new real-space configuration that can also be found under equilibrium conditions or exotic states otherwise not accessible. The details of this newly formed state will critically depend on the excitation conditions [25], finite defect density [13] or chemical doping level [26] and energy contributions from domain wall interactions [45; 46], allowing for a large parameter space to tune the macroscopic properties of this material on ultrafast time scales.