  We demonstrate the generation of photons within a fiber-cavity quantum
memory, followed by later on-demand readout. Signal photons are generated by
spontaneous four-wave mixing in a fiber cavity comprising a birefringent fiber
with dichroic reflective end facets. The detection of the partner herald photon
indicates the creation of the stored signal photon. After a delay, the signal
photon is switched out of resonance with the fiber cavity by intracavity
frequency translation using Bragg scattering four-wave mixing, driven by
ancillary control pulses. We measure sub-Poissonian statistics in the output
signal mode, with $g^{(2)}_{AC}=0.54(1)$ in the first readout bin and a readout
frequency translation efficiency of $\approx$80%. The 1/e memory lifetime is
$\approx$67 cavity cycles, or 1.68$\mu$s. In an alternate fiber cavity, we show
a strategy for noise reduction and measure $g^{(2)}_{AC}=0.068(10)$ after one
cavity cycle.
