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Doping dependence of the electron-phonon and electron-spin fluctuation interactions in the high-$T_{c}$ superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$

Using ultrafast optical techniques, we detect two types of bosons strongly coupled to electrons in the family of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ from the underdoped to overdoped regimes. The different doping dependences of the electron-boson coupling strengths enables us to identify them as phonons and spin fluctuations: electron-phonon coupling ($λ_{e-ph}$) peaks at optimal doping, and electron-spin fluctuation coupling ($λ_{e-sf}$) decreases monotonically with doping. This observation is consistent with two facts: (1) superconductivity is in close proximity with antiferromagnetism at low dopings, and (2) a pronounced lattice renormalization effect at larger dopings.