Auto-heterodyne characterization of narrow-band photon pairs

We describe a technique to measure photon pair joint spectra by detecting the time-correlation beat note when non-degenerate photon pairs interfere at a beamsplitter. The technique implements a temporal analog of the Ghosh-Mandel effect with one photon counter and a time-resolved Hong-Ou-Mandel interference with two. It is well suited to characterize pairs of photons, each of which can interact with a single atomic species, as required to study recently predicted photon-photon interaction in sub-wavelength atomic arrays. With this technique, we characterize photon pairs from cavity-enhanced parametric downconversion with a bandwidth $\approx$ 5 MHz and frequency separation of $\sim$ 200 MHz near the D$_1$ line of atomic Rb.