Ultrafast Dynamics of Correlated Electronic States in Layered Cu$_x$TiSe$_2$*

We investigate the transient optical response of electronic states in Cu$_x$TiSe$_2$ as a function of temperature and Cu doping from x=0 (semimetal and commensurate charge density wave phases) to x=0.08 (metallic and superconducting phases). We find that the cooperative driving mechanisms for the CDW, the excitonic insulator mechanism and the soft L$_1$$^-$ phonon mode, decouple at x=0.04, where fluctuations of a quantum critical point were observed in the folded Se-4p band. We also demonstrate a loss of coherence in the A$_{1g}$ phonon signal with increased Cu intercalation of the parent lattice, indicating a loss of long-range lattice order. These findings provide compelling evidence that TiSe$_2$ undergoes a quantum phase transition upon Cu intercalation from a state of commensurate charge order without superconductivity to a state with a different symmetry in which new charge order coexists with the superconducting phase.