  Identifying quantum critical points (QCPs) and their associated fluctuations
may hold the key to unraveling the unusual electronic phenomena observed in
cuprate superconductors. Recently, signatures of quantum fluctuations
associated with charge order (CO) have been inferred from the anomalous
enhancement of CO excitations that accompany the reduction of the CO order
parameter in the superconducting state. To gain more insight about the
interplay between CO and superconductivity, here we investigate the doping
dependence of this phenomenon throughout the Bi-2212 cuprate phase diagram
using resonant inelastic x-ray scattering (RIXS) at the Cu L3- edge. As doping
increases, the CO wavevector decreases, saturating at a commensurate value of
0.25 r.l.u. beyond a characteristic doping pc, where the correlation length
becomes shorter than the apparent periodicity (4a0). Such behavior is
indicative of the fluctuating nature of the CO; and the proliferation of CO
excitations in the superconducting state also appears strongest at pc,
consistent with expected behavior at a CO QCP. Intriguingly, pc appears to be
near optimal doping, where the superconducting transition temperature Tc is
maximal.
