Spontaneous Raman processes in cold atoms have been widely used in the past decade for generating single photons. Here, we present a method to optimise their efficiencies for given atomic coherences and optical depths. We give a simple and complete recipe that can be used in present-day experiments, attaining near-optimal single photon emission.
IntroductionOn-demand single photon sources are appealing ingredients for many quantum information tasks. Examples include the distribution of entanglement over long distances using quantum repeaters or quantum communications with security guarantees which remain valid, independent of the details of the actual implementation [1, 2]. These tasks necessitate stringent purity and efficiency requirements on the performance of the single photon sources used. Techniques based on spontaneous Raman processes in cold atoms are among the most advanced single-photon sources with such characteristics. The basic principle is to use an ensemble of three-level atoms in a Λ-configuration and two pulsed laser fields (see figure 1(a)). The first write pulse-the write control field-off-resonantly excites one transition, which can spontaneously produce a frequency-shifted photon-the write photon field-along the second transition through a Raman process. Since all the interacting atoms participate in the process, and there is no information about which atom emitted the photon, the detection of this write photon heralds the existence of a single delocalised excitation across the sample-an atomic spin wave. Once the spin wave has been prepared, the atomic sample is ready to be used as a source, and a second pulse-the read control field-along the second transition performs a conversion of the atomic spin wave into a second photon-the read photon field. If the duration of the process is short enough with respect to the atomic coherence times, and the optical depth of the sample sufficiently high, then the read photon is emitted efficiently in a well defined mode and the protocol provides a viable single photon source.Such sources have been at the core of numerous experiments during the last decade following the seminal paper of Duan, Lukin, Cirac and Zoller [3], showing how they could be used for long-distance quantum communication based on quantum repeater architectures (for reviews, see [4][5][6][7]). Recently, they have been used as quantum memories with storage times up to 200 ms [8,9] or as a source producing pure single photons with a temporal duration that can be varied over up to 3 orders of magnitude while maintaining constant efficiencies [10]. We stress that the efficiency of such a source is a critical parameter for the implementation of efficient quantum repeater architectures. While very high efficiencies of∼90% are essential, a reduction of the source efficiency by 1% can reduce the repeater distribution rate by 10%-20%, depending on the specific architecture [4].Several solutions can be envisioned to ensure high efficiencies. One solution relies on the use of an optical cavity to...