# Recent Progress in Multiplexed Single-Photon Sources
## 5 Theoretical Results and Experiments
### Multiplexed Single-Photon Source Experiments  
Though the idea of multiplexed SPSs is quite straightforward, the first experimental realization of such a source based on spatial multiplexing of four multiplexed units was reported only in 2011 [58]. In that experiment, a pair of beta barium borate crystals were used as parametric down-conversion sources, and the routing of the heralded photons to the output was realized by a fast, Pockels cell-based electro-optic polarization rotating switch. Multiplexing four heralded photon sources based on parametric down-conversion in waveguides was reported in 2016 [61]. In this experiment, integrated electro-optic switches were used. The advantage of using photon-number-resolving detectors in a multiplexed SPS experiment was presented in Ref. [64]. That experiment realized spatial multiplexing of two heralded sources based on spontaneous parametric down-conversion in bulk crystals. Experimental realizations of spatial multiplexing have also been reported for up to two multiplexed units by using spontaneous four-wave mixing in photonic crystal fibers and integrated opto-ceramic switches [59; 60; 63]. In all these experiments, symmetric multiplexers were used. The cited experiments successfully demonstrated the usefulness of multiplexing, though they could not exceed the overall performance of a single heralded source due to the high losses of the realized multiplexed systems. Concerning SPSs based on temporal multiplexing, six experimental realizations have been reported in the literature. In Refs. [66; 67], fiber-based systems with spontaneous four-wave mixing and integrated switches were used to realize temporally multiplexed SPSs based on storage loops with four time bins. Temporally multiplexed SPSs based on free-space storage cavities were realized by applying spontaneous parametric down-conversion for pair generation and using large-scale temporal multiplexing up to 30 [62] and 40 [70] time bins. In these experiments, low-loss Pockels cell-based optical switches were used. The scheme of the applied storage cavity is shown in Figure 6.  
Figure 5: (**a**) Achievable single-photon probability \(P_{\text{1,N}}\), (**b**) normalized second-order autocorrelation function \(g_{N}^{(2)}\), and (**c**) optimal input mean photon number \(\lambda_{\text{opt,N}}\) against the number of multiplexed units \(N\) for SPSs based on five different types of multiplexers: asymmetric multiplexer (ASYM), stepwise-optimized binary tree multiplexers (SOBTMs), minimum-based, maximum-logic output-extended incomplete binary tree multiplexers (OMAXVs), temporal multiplexers based on binary-divided delays (binary-divided) and on storage loops (loop) for the transmission coefficients \(V_{r}=0.95\) and \(V_{t}=0.95\), the detector efficiency \(V_{D}=0.9\), the general transmission coefficient \(V_{b}=0.95\), and in the case of temporal multiplexers, the transmission coefficient of one-time-bin delay \(V_{d}=0.99\) and the loss characterizing a switch at \(V_{s}=0.95\). In the scheme, the leftmost Pockels cell used to set up the polarization of the signal photon so that the neighboring polarization beam splitter either directs the photon into the storage cavity or discards it. The polarizations of the photons directed into the storage cavity are adjusted by the Pockels cell on the right so that the polarization beam splitter, which is part of the cavity, can direct the photon either to the output or back to the cavity. In the experiment of Ref. [70], an output single-photon probability \(P_{1}=0.67\) was reported that is considerably higher than that can be achieved with heralded SPSs. This single-photon probability is even higher than the best values reported for SPSs based on quantum dots [129; 130; 57; 131; 132; 133]. We note, however, that the normalized second-order autocorrelation value \(g^{(2)}=0.27\) obtained in this experiment is higher, that is, worse, compared to the value \(g^{(2)}\approx 0.02\) achieved in the cited quantum-dot based SPS experiments.