  We describe the generation of atom-resonant indistinguishable photon pairs
using nonlinear optical techniques, their spectral purification using atomic
filters, characterization using multi-photon interference, and application to
quantum-enhanced sensing with atoms. Using either type-I or type-II
cavity-enhanced spontaneous parametric down-conversion, we generate pairs of
photons in the resonant modes of optical cavities with linewidths comparable to
the 6 MHz natural linewidth of the D$_1$ line of atomic rubidium. The cavities
and pump lasers are tuned so that emission occurs in a mode or a pair of
orthogonally-polarized modes that are resonant to the D$_1$ line, at 794.7 nm.
The emission from these frequency-degenerate modes is separated from other
cavity emission using ultra-narrow atomic frequency filters, either a Faraday
anomalous dispersion optical filter (FADOF) with a 445MHz linewidth and 57 dB
of out-of-band rejection or an induced dichroism filter with an 80 MHz
linewidth and $\ge$35dB out-of-band rejection. Using the type-I source, we
demonstrate interference of photon pair amplitudes against a coherent state and
a new method for full characterization of the temporal wave-function of
narrow-band photon pairs. With the type-II source we demonstrate
high-visibility super-resolving interference, a high-fidelity atom-tuned NooN
state, and quantum enhanced sensing of atoms using indistinguishable photon
pairs.
