We report on a transient optical reflectivity study of the charge density wave (CDW) in CuxTiSe2 single crystals. Our measurements reveal that the system undergoes a quantum phase transition at x=0.04 from a strong commensurate CDW (x<0.04) to a soft incommensurate CDW (x>0.04). We find that the cooperative driving mechanisms for the commensurate CDW, the excitonic insulator mechanism and the soft L$_1$$^-$ phonon mode, decouple at x=0.04 with the observed fluctuations in the folded Se-4p band dominating the transition. We also demonstrate a loss of coherence in the A$_{1g}$ phonon with increased copper intercalation of the parent lattice, indicating a loss of long-range lattice order. These findings provide compelling evidence that TiSe2 undergoes a quantum phase transition upon copper intercalation from a state of commensurate charge order to a state with a different symmetry in which the new charge order coexists with the superconducting phase.
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