Ultrabright omnidirectional collective emission of correlated photon Pairs from atomic vapors

Spontaneous four-wave mixing can generate highly correlated photon pairs from atomic vapors. We show that multiphoton pumping of dipole-forbidden transitions in a recoil-free geometry can result in ultrabright pair emission in the full 4π solid angle, while strongly suppressing background Rayleigh scattering and associated atomic heating, Such a system can produce photon pairs at rates of ~1012 per second, given only moderate optical depths of 10-100, or alternatively, the system can generate paired photons with subnatural 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 Cs133 and Yb171 level structures. Last, we demonstrate that dark-state adiabatic following electromagnetically induced transparency and/or time-scale hierarchy protects the paired photons from reabsorption as they propagate through the optically thick sample.