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 fields 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.
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