Fast Entanglement Distribution with Atomic Ensembles and Fluorescent Detection

Supplementary EPAPS Document J. B. Brask,1 L. Jiang,2 A. V. Gorshkov,2 V. Vuletic,3 A. S. Sørensen,1 and M. D. Lukin2 1QUANTOP, The Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen Ø, Denmark 2Department of Physics, Harvard University, Cambridge, MA 02138, USA 3Harvard-MIT Center for Ultracold Atoms, Department of Physics, MIT, Cambridge, MA 02139, USA (Dated: September 29, 2009) In this supporting material, we provide details about how the rates and rate improvements shown in Fig. 3 of the paper were obtained. In Fig. 3 of the paper we compare the rates achieved by our new scheme to those of previous proposals based on retrieval and single-photon detection. We consider schemes where no dark counts occur, and where the dominant error comes from multiexcitation events during entanglement generation. As explained in the main body of the paper, this is justi ed for our new protocol when puri cation by interrupted retrieval (PIR) is employed and the upper and lower bounds on the number of atoms are compatible. For the reference schemes, the assumption of no dark counts corresponds to an ideal situation. We also assume photon-number resolving detectors. Again, this corresponds to an ideal situation for the single-photon detections of the reference schemes, while for uorescence detection, it is realistic to distinguish di erent occupation numbers for the relevant atomic levels. I. SINGLE-RAIL The single rail scheme considered in the paper is the original DLCZ scheme, proposed by Duan et al. in Ref. [1]. A generalised variant of this scheme was analysed in Ref. [5]. In that work, analytic expressions were derived for the rate and the quality of nal entangled pairs in the DLCZ scheme under various conditions. The quality of entanglement was given in terms of a Bell parameter pertaining to a CHSH-type inequality. If we instead compute a more common gure of merit the delity with respect to a maximally entangled Bell state the expressions in the absence of dark counts become