Persistent short-range charge correlations revealed by ultrafast melting of electronic order in YBa$_2$Cu$_3$O$_{6+x}$
Charge density waves (CDW) are ubiquitous in the complex phase diagram of cuprate superconductors and exhibit both short- and long-range correlations. Using time-resolved resonant X-ray scattering, we investigate the photo-induced dynamics of CDW in YBa$_2$Cu$_3$O$_{6.67}$. We discover an excitation threshold ($\Phi$$_\mathrm{C}$ $\approx$ 65 $\mu$J/cm$^2$) above which long-range CDW disappear, revealing a persistent CDW peak with short-range correlation length. Ultrafast photo-excitation promptly uncovers this residual short-range CDW correlations, appearing within $\approx$ 0.2 ps. Long-range CDW coherence recovers within $\approx$ 0.6 ps, while the peak intensity remains partially suppressed. We rationalize the dichotomic behavior in the fluence and temporal dependencies as the signature of two coexisting CDW peaks, arising from short- and long-range correlations, which we disentangle through their distinct response to photo-excitation. We provide evidence that the collapse of long-range correlations is driven by an electronic process, while short-range correlations are characterized by distinct timescales and stiffness against photo-excitation. This approach establishes ultrafast X-ray scattering as an effective tool for disentangling coexisting density waves and correlations in quantum materials.