  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.
