  We report a bright photon-pair source with a coincidence counting rate per
input power (cps/mW) of tens of thousands, obtained via spontaneous four-wave
mixing from a Doppler-broadened atomic ensemble of the 5S1/2-5P3/2-5D5/2
transition of 87Rb. The photon-pair generation rate is enhanced by the
two-photon coherence contributions from almost all the atomic velocity groups
in the Doppler-broadened ladder-type atomic system. We obtained the violation
of the Cauchy-Schwarz inequality by a factor of 2370(150). We believe that our
scheme for highly bright paired photons is important as a useful quantum light
source for quantum entanglement swapping between completely autonomous sources.
