Quantum Repeaters with Photon Pair Sources and Multimode Memories

We propose a quantum repeater protocol which builds on the well-known Duan-Lukin-Cirac-Zoller (DLCZ) protocol [L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature (London) 414, 413 (2001)], but which uses photon pair sources in combination with memories that allow to store a large number of temporal modes. We suggest to realize such multimode memories based on the principle of photon echo, using solids doped with rare-earth-metal ions. The use of multimode memories promises a speedup in entanglement generation by several orders of magnitude and a significant reduction in stability requirements compared to the DLCZ protocol.

Figure 1

Quantum repeater scheme using pair sources and multimode memories. (a) The sources $S_A$ and $S_B$ can each emit a photon pair into a sequence of time bins. The detection of a single photon behind the beam splitter at the central station projects the memories $M_A$ and $M_B$ into an entangled state Eq. (2). (b) If entangled states have been established between the $m$th time bins in $M_A$ and $M_B$ and between the $n$th time bins in $M_C$ and $M_D$, an entangled state between the $m$th time bin in $M_A$ and the $n$th time bin in $M_D$ can be created by reconverting the memory modes into photonic modes and combining the appropriate time bins on a beam splitter. (c) Useful entanglement can be created between two pairs of distant memories as in Ref. 2. Again the appropriate time bins have to be combined on beam splitters.

Figure 2

The maximum achievable average efficiency ${\overline{\eta }}_M$ as a function of $y={\alpha }_{0}L/N$. One can see that ${\overline{\eta }}_M=0.9$ is obtained for $y=30$. This implies that storing $N=100$ time bins with this average efficiency requires ${\alpha }_{0}L=3000$, while 1000 time bins require ${\alpha }_{0}L=30000$; ${\overline{\eta }}_M=0.95$ is obtained for $y=50$. The required values of $x={\gamma }_{0}N\Delta t$ are $x=0.8$ for ${\overline{\eta }}_M=0.9$ and $x=0.6$ for ${\overline{\eta }}_M=0.95$.