On-demand superradiant conversion of atomic spin gratings into single photons with high efficiency

We create quantized spin gratings by single-photon detection and convert them on demand into photons with retrieval efficiencies exceeding 40% (80%) for single (a few) quanta. We show that the collective conversion process, proceeding via superradiant emission into a moderate-finesse optical resonator, requires phase matching. The storage time of 3 micros in the cold-atom sample, as well as the peak retrieval efficiency, are likely limited by Doppler decoherence of the entangled state.