  We report a highly efficient source of narrow-band photon pairs based on
parametric down-conversion in a crystalline whispering gallery mode resonator.
Remarkably, each photon of a pair is strictly emitted into a single spatial and
temporal mode, as witnessed by Glaubers autocorrelation function. We explore
the phase-matching conditions in spherical geometries, and determine the
requirements of the single-mode operation. Understanding these conditions has
allowed us to experimentally demonstrate a single-mode pair-detection rate of
$0.97 \cdot 10^6$ pairs/s per mW pump power per 20 MHz bandwidth without the
need of additional filter cavities.
