## 5 Conclusions and Discussion  
We demonstrate the frequency conversion interface from rubidium D1 line to communication L-band by using DFG process in PPLN waveguide. In order to suppress broadband SRS noise produced by the pumping field, we design a hierarchical filtering system to narrow the noise bandwidth to 11.7 MHz. To our knowledge, this is the narrowest filtering bandwidth applied in frequency down conversion. The filtering system includes a bandpass filter, an FBG, two cascaded etalons and a confocal F-P cavity with low finesse. These optical components are easy to use, so the filtering method is suitable to be popularized in the experimental research of frequency conversion. We study the influence of the filtering system on the output pulse shape, and find that the shape of input Gaussian pulse can be preserved when its temporal FWHM is not less than 100 ns. Benefiting from the strong noise suppression, even at such low external device conversion efficiency (0.51%) and large duration (\(\Delta t_{in}=250\) ns) of the input pulse, the average photon number contained in the input pulse \(\mu_{1}<1\) to require the SNR of converted pulse equal to 1. At present, using bridge PPLN waveguide, the external conversion efficiency of DFG can reach more than 30% [15; 23; 28]. If our filtering system is combined with such an efficient bridge waveguide, it is predicted that the SNR of the converted pulse with \(\Delta t_{in}=100\) ns and \(\mu_{in}=1\) will exceed 20, which can be used as the frequency conversion interface in fiber quantum networks. At present, the transmittance of our filtering system is only 11%. The low transmittance will reduce the rate of entanglement distribution in quantum network. We propose a scheme to improve the performance of the filtering system. If we add two additional etalons with length of 5.4 mm and 7.5 mm (finesse of 30) to the filtering system, the noise suppression range of the cascaded four etalons is extended to 2000 GHz (17 nm). In this way, the Bragg fiber grating can be removed in the filtering system. Thus, the filtering system consists of four etalons, an F-P cavity, two DMs and two band-pass filters. It is not difficult to optimize the single etalon efficiency to 95% and the F-P cavity efficiency to 90%. By choosing DMs and band-pass filters with high transmittance (>99%), the overall throughput of the filtering system can reach 70%. By using the frequency conversion interface, we calculate the needed time for entanglement establishment between two remote quantum nodes based on DLCZ (for Duan, Lukin, Cirac, and Zoller) quantum repeater scheme [4]. In the scheme the success probability for entanglement generation is expressed as \(P_{0}=\left(\chi^{2}e^{-L_{0}/L_{att}}\eta_{FC}^{2}\eta_{TD}^{2}\right)/2\), where \(\chi\) is the excitation probability of Stokes photon, \(L_{0}\) is the distance between the two nodes, \(L_{att}\) is the attenuation length of the fiber channel, \(\eta_{FC}\) is the efficiency of frequency conversion module, and \(\eta_{TD}\) is the total detection efficiency. The needed time for a single entanglement generation attempt is \(T_{0}=T_{cc}/P_{0}\), where \(T_{cc}=L_{0}/c\) is the communication time interval and \(c\) is the light speed in fiber. Combining a frequency conversion module with an efficiency of 30% and a narrow-band filter system with an efficiency of 70% to form a quantum frequency conversion interface, the whole efficiency of the interface is 21%. When such an interface is used for quantum repeater, the photon at L-band is used for remote transmission and the transmission loss in fiber is ~0.18 dB/km. The needed time for entanglement generation between two quantum nodes 50 km apart is 38 s with \(\chi=3.8\%\), \(\eta_{FC}=30\%\), and \(\eta_{TD}=90\%\). If a photon at 795 nm is directly transmitted over a long distance without frequency conversion interface (transmission loss ~4 dB/km), the time required to establish entanglement is \(4.3\times 10^{19}\) s with same \(L_{0}\), \(\chi\) and \(\eta_{TD}\).