Enhancing Multiphoton Rates with Quantum Memories

Single photons are a vital resource for optical quantum information processing. Efficient and deterministic single photon sources do not yet exist, however. To date, experimental demonstrations of quantum processing primitives have been implemented using nondeterministic sources combined with heralding and/or postselection. Unfortunately, even for eight photons, the data rates are already so low as to make most experiments impracticable. It is well known that quantum memories, capable of storing photons until they are needed, are a potential solution to this “scaling catastrophe.” Here, we analyze in detail the benefits of quantum memories for producing multiphoton states, showing how the production rates can be enhanced by many orders of magnitude. We identify the quantity $\eta B$ as the most important figure of merit in this connection, where $\eta$ and $B$ are the efficiency and time-bandwidth product of the memories, respectively.

Figure 1

An array of $N$ heralded parametric sources synchronized by quantum memories. The sources are repeatedly pumped, and each photon emitted is stored until all but one of the memories are charged. Then emission of a photon by the final source triggers retrieval from the memories, in order to generate an $N$-fold coincidence.

Figure 2

Multiphoton waiting times. The blue bars (top row) show the average waiting time between $N$-photon events for a system of $N$ unsynchronized down-conversion sources, assuming negligible dark counts ($d=0$), a pulse repetition rate of $\mathcal{R}=1\mathrm{GHz}$, a heralding efficiency of $h=50\%$, and a threshold fidelity $\Theta =90\%$. The red bars (middle row) show the corresponding waiting times when the system is synchronized, with memory efficiencies ${\eta }_s={\eta }_r=75\%$ and a time-bandwidth product $B=1000$, where postselection on at least $N$ photons is used (we set $p_{\Theta }$ so that $\tilde{\mathcal{F}}=\Theta$). The green bars (bottom row) show the waiting times without postselection (we set $p_{\Theta }$ so that $\mathcal{F}=\Theta$), where to achieve the required unpostselected fidelity threshold we now assume memory efficiencies of ${\eta }_s={\eta }_r=99\%$.