# Recent Progress in Multiplexed Single-Photon Sources
## 5 Theoretical Results and Experiments
### Multiplexed Single-Photon Source Experiments
Accordingly, the fidelity of the output photon state is lower for this multiplexed source due to the higher multi-photon contribution. Note that there is a tradeoff between the second-order autocorrelation function \(g^{(2)}\) and the single-photon probability \(P_{1}\). The value of \(g^{(2)}\) can be reduced by decreasing the input mean photon number \(\lambda\), which generally leads to a decrease in the single-photon probability \(P_{1}\). This decrease can be reduced by the reoptimization method described in Section 5.1 and originally introduced in Ref. [57]. In a recent experiment, a telecom wavelength temporally multiplexed integrated SPS based on a silicon waveguide and a low-loss fiber switch and loop architecture has been presented [134]. In this experiment, a value \(g^{(2)}(0)=0.01\) of the normalized second-order autocorrelation function was achieved, which is comparable to the values obtained with quantum dot sources. The single-photon probability of this source was rather low (\(P_{1}\approx 0.015\)), though this system achieved a factor \(4.5\pm 0.5\) enhancement of the single-photon probability of the heralded source used. In Ref. [135], a telecom wavelength continuous wave temporally multiplexed SPS based principally on fiber-integrated components and applying two time bins was demonstrated. The latter two experiments are important steps toward the development of integrated telecom-wavelength SPSs that can be applied in practical quantum communication. Combined multiplexing was also successfully realized in an experiment reported in Ref. [65]. In that experiment, two heralded SPSs based on parametric down-conversion were multiplexed spatially and then temporally using binary-divided delay lines realizing four time bins. Regarding spectrally multiplexed SPSs, four experimental realizations have been published thus far [68; 69; 71; 72]. In these experiments, only three spectral modes have been multiplexed, probably because increasing the number of multiplexed spectral modes can be technically challenging. Finally, we note that all the available experimental data concerning the multiplexed experiments reviewed here have been presented in a table of Ref. [9] except for data of the experiments presented in Refs. [134; 135]. In addition to the single-photon probability (brightness) of the source and the second-order correlation function, the single-photon rate  
Figure 6: Schematic figure of a storage cavity with Pockels cell-based optical switches. PBSs denote polarizing beam splitters; PCs are Pockels cells. is an important data measurement characterizing SPSs. The best value of the single-photon rate (130 kHz) was achieved with the temporally multiplexed SPS of Ref. [70] that also produced the highest single-photon probability (\(P_{1}=0.67\)), as was pointed out above. The experiments reviewed in this section used various types of sources, switches, and detectors. All these elements are available both in bulk optic and integrated forms. A detailed evaluation and comparison of the different realizations of these elements can be found in Ref. [9]. As we have described earlier, the performance of a multiplexed SPS is basically determined by the losses of the components forming the multiplexed units and the multiplexer. The losses of integrated switches are significantly higher than those of bulk switches, but they can be faster than the bulk ones. Additional losses appear in integrated sources when disparate elements are coupled and also at coupling of bulk optic elements to integrated ones. Nevertheless, integrated optical devices can be easily adapted to practical applications due to their compactness and robustness. Hence, the development of multiplexed SPSs realized with integrated optical elements is an important research topic.