  Spontaneous four-wave mixing can generate highly correlated photon pairs from
atomic vapors. We show that multi-photon pumping of dipole-forbidden
transitions in a recoil-free geometry can result in ultra-bright pair-emission
in the full 4\pi solid angle, while strongly suppresses background Rayleigh
scattering and associated atomic heating, Such a system can produce photon
pairs at rates of ~ 10 ^12 per second, given only moderate optical depths of 10
~ 100, or alternatively, the system can generate paired photons with
sub-natural bandwidths at lower production rates. We derive a rate-equation
based theory of the collective atomic population and coherence dynamics, and
present numerical simulations for a toy model, as well as realistic model
systems based on 133 Cs and 171 Yb level structures. Lastly, we demonstrate
that dark-state adiabatic following (EIT) and/or timescale hierarchy protects
the paired photons from reabsorption as they propagate through an optically
thick sample.
