  High efficiency, sub-MHz bandwidth photon pair generators will enable the
field of quantum technology to transition from laboratory demonstrations to
transformational applications involving information transfer from photons to
atoms. While spontaneous parametric processes are able to achieve high
efficiency photon pair generation, the spectral bandwidth tends to be
relatively large, as defined by phase-matching constraints. To solve this
fundamental limitation, we use an ultra-high quality factor (Q) fused silica
microsphere resonant cavity to form a photon pair generator. We present the
full theory for the SWM process in these devices, fully taking into account all
relevant source characteristics in our experiments. The exceptionally narrow
(down to kHz-scale) linewidths of these devices in combination with the device
size results in a reduction in the bandwidth of the photon pair generation,
allowing sub-MHz spectral bandwidth to be achieved. Specifically, using a pump
source centered around 1550nm, photon pairs with the signal and idler modes at
wavelengths close to 1540nm and 1560nm, respectively, are demonstrated. We
herald a single idler-mode photon by detecting the corresponding signal photon,
filtered via transmission through a wavelength division multiplexing channel of
choice. We demonstrate the extraction of the spectral profile of a single peak
in the single-photon frequency comb from a measurement of the signal-idler time
of emission distribution. These improvements in device design and experimental
methods enabled the narrowest spectral width (366kHz) to date in a heralded
single photon source basedon SFWM.
