Doping dependence of the electron-phonon and electron-spin fluctuation interactions in Bi-2212

In the BCS theory of conventional superconductors, electrons form (Cooper) pairs via interactions with the underlying crystal lattice. In the cuprate superconductors, it is not clear whether Cooper pairing takes place via electrons interacting with phonons, spin fluctuations, or whether a bosonic mechanism is necessary at all. Though time-integrated optical measurements on the cuprates can give information on the coupling strength between electrons and an effective boson, it is difficult to tell whether one or more bosons are involved, or the nature of these bosons. We report measurements of time-resolved quasiparticle relaxation of Bi$_2 $Sr$_2 $CaCu$_2 $O$_{8+\delta } $ single crystals (hole concentration $p$ = 0.10-0.22). Our data indicate that \textit{two} bosonic modes are associated with superconductivity: the electron-phonon coupling constant ($\lambda _{e-ph} )$ peaks at optimal doping, while the electron-spin fluctuation coupling constant ($\lambda _{e-sf} )$ decreases monotonically with doping.