  Photonics is a promising platform for quantum technologies. However, photon
sources and two-photon gates currently only operate probabilistically.
Large-scale photonic processing will therefore be impossible without a
multiplexing strategy to actively select successful events. High
time-bandwidth-product quantum memories - devices that store and retrieve
single photons on-demand - provide an efficient remedy via active
synchronisation. Here we interface a GHz-bandwidth heralded single-photon
source and a room-temperature Raman memory with a time-bandwidth product
exceeding 1000. We store heralded single photons and observe a clear influence
of the input photon statistics on the retrieved light, which agrees with our
theoretical model. The preservation of the stored field's statistics is limited
by four-wave-mixing noise, which we identify as the key remaining challenge in
the development of practical memories for scalable photonic information
processing.
