  Hybridization of Bogoliubov quasiparticles (BQPs) between the CuO$_2$ layers
in the triple-layer cuprate high-temperature superconductor
Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ is studied by angle-resolved
photoemission spectroscopy (ARPES). In the superconducting state, an
anti-crossing gap opens between the outer- and inner-BQP bands, which we
attribute primarily to interlayer single-particle hopping with possible
contributions from interlayer Cooper pairing. We find that the $d$-wave
superconducting gap of both BQP bands smoothly develops with momentum without
abrupt jump in contrast to a previous ARPES study. Hybridization between the
BQPs also gradually increases in going from the off-nodal to the anti-nodal
region, which is explained by the momentum-dependence of the interlayer
single-particle hopping. As possible mechanisms for the enhancement of the
superconducting transition temperature, the hybridization between the BQPs, as
well as the combination of phonon modes of the triple CuO$_2$ layers and spin
fluctuations are discussed.
