  We demonstrate the storage and on-demand retrieval of single-photon-level
telecom pulses in a fiber cavity. The cavity is formed by fiber Bragg gratings
at either end of a single-mode fiber. Photons are mapped into, and out of, the
cavity using quantum frequency conversion driven by intense control pulses. In
a first, spliced-fiber, cavity we demonstrate storage up to 0.55$\mu$s (11
cavity round trips), with $11.3 \pm 0.1$% total memory efficiency, and a
signal-to-noise ratio of $12.8$ after 1 round trip. In a second, monolithic
cavity, we increase this lifetime to 1.75$\mu$s (35 round trips) with a memory
efficiency of $12.7 \pm 0.2%$ (SNR of $7.0 \pm 0.2$) after 1 round trip.
Fiber-based cavities for quantum storage at telecom wavelengths offer a
promising route to synchronizing spontaneous photon generation events and
building scalable quantum networks.
