## 4 Conversion Device Characterization  
On the basis of the strong noise filtering, we study the characteristics of the frequency conversion devices. Firstly, we measured the detection probability of the converted pulse \(D_{s}\) in terms of the pumping power \(P_{P}\), shown by the blue squares in Figure 5a. Here, the average photon number contained in the input pulse is \(\mu_{in}=5\). The temporal FWHM of the 795 nm input pulse is taken as 100 ns, and the measuring window width is 400 ns. The pink circles in Figure 5a show the noise detection probability \(D_{n}\) when only the pumping beam is injected. The red triangles represent the net signal detection probability \(D_{s}-D_{n}\). Limited by the maximum allowable power of fiber end face, the maximum pumping power coupled into the \(2\times 1\) combiner \(P_{P}\) is 350 mW. The signal (noise) detection probability \(D_{s}\) (\(D_{n}\)) increases almost linearly with the pumping power within the current power range of the pumping light. The net signal \(D_{s}-D_{n}\) is close to \(D_{s}\) due to the extremely low noise level even at \(P_{P}=350\) mW (\(D_{s}=0.57\%\), \(D_{n}=0.028\%\)). The total conversion efficiency including all losses can be calculated by \(\eta_{tot}=(D_{s}-D_{n})/\mu_{in}\), and \(\eta_{tot}^{max}=1.08\times 10^{-3}\) at \(P_{P}=350\) mW. By correcting for the quantum efficiency of SPD (20%), the maximum external device conversion efficiency \(\eta_{ext}^{max}=0.54\%\), which can be interpreted as the probability to find a photon at the output of the converted device (including the filtering system) with \(\mu_{in}=1\). Next, by further correcting for the transmission of the filtering system (11%), we calculate the conversion efficiency of the fiber-coupled PPLN waveguide module (\(\eta_{lay}^{max}=4.9\%\)), corresponding to \(\mu_{out}/\mu_{in}\), where  
Figure 4: The influence of the three-stage filtering system on the temporal shape of converted pulse. The gray columns are the photon statistics distributions of the converted fields measured by SPD with input FWHM of \(\Delta t_{in}\). Red solid lines are the fitted Gauss distributions with FWHM of \(\Delta t_{out}\). (a) \(\Delta t_{in}=53\) ns, \(\Delta t_{out}=102\) ns. (b) \(\Delta t_{in}=112\) ns, \(\Delta t_{out}=133\) ns. (c) \(\Delta t_{in}=182\) ns, \(\Delta t_{out}=190\) ns. The pumping power is 350 mW. The counts is the accumulation of \(5\times 10^{5}\) repeated measurements. Figure 5: (a) Detection probability with (\(D_{s}\), blue squares) and without (\(D_{n}\), pink circles) input signal (\(\mu_{in}=5\) ) as a function of the pumping power \(P_{P}\). The red triangles are the net signal (\(D_{s}-D_{n}\) ). (b) The SNR of the converted field after the filtering system as a function of the pumping power \(P_{P}\) (red squares, right axis). The external device conversion efficiency \(\eta_{ext}\) is shown by the blue circles on the left axis. \(\mu_{out}\) is the average photon number of the converted pulse at the output of the conversion module. Finally, it can be deduced that the maximum conversion efficiency inside the waveguide \(\eta_{int}^{max}=20.4\%\), by considering the transmission efficiency of the \(2\times 1\) combiner (0.67), the input coupling efficiency of the waveguide (0.55), and the output coupling efficiency of waveguide (0.65). According to \(SNR=(D_{s}-D_{n})/D_{n}\), we calculate the SNR of the converted pulse (\(\mu_{in}=5\)) after the filtering system, shown in Figure 5b. The SNR increases with the pumping power in the current power range of the pumping light, and the SNR achieves 19.4 at \(P_{P}=350\) mW. From Figure 5b we can see that SNR and the external device conversion efficiency have the same growth trend as the pumping power increases due to low noise level. In general, the pumping power at the optimal SNR is much lower than that at the maximum conversion efficiency [23; 29]. The reduction in noise level is beneficial to the simultaneous optimization of SNR and conversion efficiency.