1. Introduction

Quantum repeaters for efficiently transmitting a quantum state through lossy and noisy quantum channels have been proposed [1] and actively studied for realizing long distance quantum communication [2]. In the quantum repeater protocols, photons entangled with quantum memories at remote parties are sent to relay points, and they are measured by the Bell measurement for establishing the entanglement between the quantum memories at the remote parties. The elementary part that creates entanglement between a quantum memory and a photon has been demonstrated in atomic systems [3, 4], trapped ion systems [5] and solid-state systems [6, 7]. In such systems, the wavelengths of the photons are strictly limited by the structure of their energy levels, which lie around visible range. On the other hand, when we look at optical-fiber networks, the photons at the telecommunication wavelengths are crucial for the efficient transmission of the photons. Thus a photonic quantum interface [8] for visible-to-telecommunication wavelength conversion is considered to be inevitable for a long distance quantum communication based on the quantum repeaters [9].

So far, in order to build such a quantum interface, the frequency down-conversion working at a single-photon level from visible to the telecommunication wavelengths has been actively studied by using nonlinear optical media [10–17]. In the first experimental demonstration employing a light field with a non-classical property, the wavelength of 795 nm which corresponds to the D1 line of the rubidium atoms are converted to 1367 nm by using a third-order optical nonlinearity in a rubidium atomic cloud [10, 11]. In [11], preservation of the entanglement between two photons after the frequency down-conversion was also observed. For a wide-band and a compact wavelength conversion, the difference frequency generation (DFG) via a second-order optical nonlinearity in a periodically-poled lithium niobate (PPLN) has been used and the preservation of the quantum state through the wavelength conversion from 780 nm which corresponds to the D2 line of the rubidium atom to 1522 nm has been demonstrated [15, 17]. The non-classical property of a light converted to 1313 nm from a 711 nm light emitted by a quantum dot has also been demonstrated [16]. In [14], the feasibility of the frequency down-conversion of a light at a single-photon level from 738 nm to 1557 nm by using the 1403 nm pump light has been shown for single-photon sources based on silicon-vacancy centers in diamond [18].

Another important wavelength which should be converted to the telecommunication bands for quantum communications is 637 nm corresponding to the resonant wavelength of the nitrogen-vacancy (NV) center in diamond [19]. The NV center in diamond is one of the promising candidates for the quantum memories with the ability to create the entanglement with photons [6]. In spite of a variety of demonstrations related to the NV centers in diamond in recent years [20–27], to the best of our knowledge, none of the demonstration of the frequency down-conversion from 637 nm to the telecommunication bands with the preservation of the non-classical property and/or the quantum information of the input light has been performed. In the experiment in [28], while the conversion from 633 nm to 1.56-μm has been observed with a 1.06-μm pump light, the signal-to-noise ratio (SNR) was not sufficient for the observation of the above mentioned properties.

In this paper, we demonstrate a low-noise wavelength conversion of a 637 nm light at a single-photon level to the telecommunication band by using a PPLN waveguide for realizing the efficient optical-fiber quantum communication based on NV centers in diamond [9]. The converted wavelength in this experiment is 1587 nm which is determined by the wavelength of 1064 nm of the cw pump light. In the experiment, we evaluate the performance of the wavelength converter, namely we clarify the overall conversion efficiency of the signal light and the amount of background photons induced by the conversion process. From the experimental results, we derive the intensity correlation and the average photon number of a converted telecom light pulse which are decided by those of a 637 nm input light pulse and the intrinsic property of the converter. Then we discuss the feasibility of the observation of non-classical property of the telecom light after the frequency down-conversion from a 637 nm light pulse. We found that when the transform-limited light pulse from the NV centers in diamond with a lifetime of 13.7 ns reported in [23,24] is prepared with a probability above 10⁻³, the intensity correlation of the converted telecom photon will be below 0.8 which indicates the non-classical property of the converted light.

2. Experiment

2.1. Experimental setup

The experimental setup is shown in Fig. 1. The 637 nm signal light is taken from a vertical (V) polarized cw external cavity laser diode with the linewidth of < 150 MHz and a maximum power of 9 mW. The power of the signal light input to the PPLN waveguide is adjusted by using a variable attenuator (VA) within the range from 1mW to a photon rate of 40 MHz. We use a cw pump laser with the center wavelength of 1064 nm and the linewidth of < 100 MHz for the wavelength conversion. The power of the pump laser coupled to the PPLN waveguide is varied up to ≈ 0.4 W by a polarization beamsplitter (PBS) and a half-wave plate (HWP). The pump beam is set to the vertical polarization by a HWP and then it is combined with the signal beam by a dichroic mirror. The two beams are coupled to the PPLN waveguide by using an aspheric lens (L1) of f = 8mm with anti-reflective coating for both the signal light and the pump light.

 

Fig. 1 Experimental setup. The cw signal light at 637 nm is frequency down-converted to 1587 nm by using a strong cw pump light at 1064 nm. The converted light is diffracted by the two Bragg gratings (BG_T) and detected by the SSPD.

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The PPLN waveguide we used is ridged-type waveguide, and its cross section is a square with side lengths of 8 μm. The PPLN as the core layer is Zn-doped, and the material of the cladding layer is lithium tantalite. They are combined by the direct bonding technique [29]. The length of the waveguide is 23 mm. The period of periodically-poled structure is 11.5 μm. Due to the type-0 quasi-phase matching condition, the V-polarized signal photon at 637 nm is converted to the V-polarized telecom photon at 1587 nm with the V-polarized strong pump beam at 1064 nm. The temperature is controlled to be ≈ 20°C. The phase-matching bandwidth for 637 nm signal light of this waveguide is calculated to be ≈ 0.1 nm.

The output photons from the PPLN waveguide are collimated by an aspheric lens (L2) of f = 8mm with anti-reflective coating for the signal light, pump light and telecom light. Two Bragg gratings (BG_T) with a bandwidth of 1 nm extract only the converted telecom light among them. The combined bandwidth of two BG_T is Δ̃ ≈ 0.7 nm. The telecom light is coupled to the single-mode fiber (D_T), and detected by a superconducting single-photon detector (SSPD) after passing through an attenuator of ≈ 10 dB for preventing the saturation of the detection counts. The SSPD has a cavity structure and its quantum efficiency denoted by ε is ≈ 0.6 [30].

2.2. Experimental results

In order to estimate an internal conversion efficiency of the frequency down-converter and an amount of background photons generated by the conversion process, we first estimate the transmittance of the overall optical circuit by measuring the power of the light before and after the optical components. The coupling efficiency of the signal light to the PPLN waveguide is T_in ≈ 0.88. The diffraction efficiency of each of BG_T is T_BG ≈ 0.86. The telecom photons diffracted by the last BG_T pass through the HWP and PBS, and then enter D_T. The efficiency of these processes is estimated to be ≈ 0.42. As a result, the transmittance of the optical circuit from the first BG_T to the front of the fiber attenuator is T_oc ≈ 0.31. The transmittance of the fiber attenuator is T_att ≈ 0.083.

The internal conversion efficiency in the PPLN depending on the pump power is estimated by the observed output power of the converted light coupled to D_T connected to a power meter instead of the fiber attenuator and the SSPD in Fig. 1. In this measurement, we set the power of the input light at 637 nm coupled to the PPLN waveguide to be ≈ 0.84 mW. From the observed values by the power meter and the estimated transmittance T_oc of the optical components, we estimate the internal conversion efficiencies of the photon number. The result is shown in Fig. 2. The conversion efficiency of the DFG process with a strong pump light is expected to be proportional to ${\text{sin}}^2(\sqrt{\kappa P})$ [8], where P represents the pump power. The best fit to the observed conversion efficiency with ${\eta }_{\text{conv}}={\eta }_{\text{conv}}^{\text{max}}{\text{sin}}^2(\sqrt{\kappa P})$ gives ${\eta }_{\text{conv}}^{\text{max}}\approx 0.44$ and κ ≈ 5.8/W. The best conversion efficiency of 0.44 will be achieved at a pump power of ≈ 0.43 W.

 

Fig. 2 (a) Conversion efficiency from 637 nm to 1587 nm as a function of the pump power P. The curve fitted to the experimental data is described by ${\eta }_{\text{conv}}^{\text{max}}{\text{sin}}^2(\sqrt{\kappa P})$ with ${\eta }_{\text{conv}}^{\text{max}}\approx 0.44$ and κ ≈ 5.8/W.

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We evaluate the amount of background photons at the down-converted wavelength of 1587 nm. The background photons were measured when we turned off the signal light and input only the pump light to the PPLN waveguide. Before we investigate the dependency of the background photons on the pump power, we first see the polarization property of the background photons, which was performed by measuring the background photon counts with various rotation angles of the HWP in front of the last PBS. This measurement was performed at 0.30 W pump power. The experimental result of the count rate of the background photons depending on the rotation angle is shown in Fig. 3(a). The degree of polarization of the background photons was ≈ 0.95. The standard deviations of the observed values under the assumption of the Poisson statistics of the observed counts are less than 0.01. We note that when we measured the polarization property for the signal light, the degree of the polarization of the signal photons was over 0.99 by subtracting the effect of the background photons from the observed counts. From the result, we see that while the polarization of the background photons is almost V, a small number of the background photons are orthogonal to V polarization. In the following experiment, H polarization component of the background photons is reflected by the PBS in front of D_T.

 

Fig. 3 (a) The observed count rates of the background photons (blue circle) and the signal photons (red triangle) depending on the rotation angle of the HWP followed by the PBS and the detector. We used the 0.30 W pump power for the measurement. The degrees of polarization of the background photons and the signal photons were 0.95 and over 0.99, respectively. The result shows that the background photons include the H polarization. (b) The dependency of the background photon rate on the pump power when the angle of the HWP is 0. By using the dark count rate of d = 220 Hz, the background photon rate is fitted to the line described by BP + d with B ≈ 135 Hz/mW.

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The dependency of the background photon rate on the pump power is shown in Fig. 3(b). We see that the background photon rate linearly increase with the pump power. From this, we infer that the main cause of the noises is the Raman scattering of the strong pump light as reported in the previous experiments of the frequency down-conversion [14, 17]. In order to fit the data, we use the linear function of the photon count rate written as N = BP + d, where d = 220 Hz is determined by an observed value of the dark count rate of the SSPD. The coefficient B is estimated to be 135 Hz/mW. The internal background photon rate of the converter is B/(T_ocT_attε) ≈ 9 × 10³ Hz/mW. As a reference, we compare the intrinsic background photon generation rate due to the Raman scattering in this experiment with that in the demonstration for frequency down-conversion from 780 nm to 1522 nm in [15,17] when these converters give the same internal conversion efficiency. The observed value of the Raman scattering in [17] was B₇₈₀ = 80Hz/mW which was detected by a photon detector with the quantum efficiency of 0.125. In the report, the overall conversion efficiency just before the photon detector was 0.005 which includes the internal conversion efficiency of 0.07. From these values, the internal background photon rate is roughly estimated to be ≈ 9 × 10³ Hz/mW. The conversion efficiency for the cw signal light was ${\eta }_{\text{conv},780}={\eta }_{\text{conv},780}^{\text{max}}{\text{sin}}^2(\sqrt{{\kappa }_{780}P})$ with ${\eta }_{\text{conv},780}^{\text{max}}\approx 0.71$ and κ₇₈₀ ≈ 3.6/W [15, 17]. When the conversion efficiencies of the two converters are the same, the ratio of the background photon rate of the converter for the 637 nm light to that for the 780 nm light takes a maximum for ${\eta }_{\text{conv}}={\eta }_{\text{conv},780}={\eta }_{\text{conv}}^{\text{max}}$. For the converter in [15, 17], ${\eta }_{\text{conv},780}={\eta }_{\text{conv}}^{\text{max}}$ is achieved at a pump power of ≈ 0.23 W, resulting in the background photon rate of ≈ 2.1 × 10⁶ Hz. For the converter in this paper, ${\eta }_{\text{conv}}={\eta }_{\text{conv}}^{\text{max}}$ is given by the pump power of ≈ 0.43 W, resulting in the background photon rate of ≈ 3.7 × 10⁶ Hz. By using these values, the background photon rate introduced by the conversion process in this experiment is, at the most, twice as large as that in [15, 17].

3. Discussion

In this section, we discuss the performance of the demonstrated frequency down-converter for a pseudo single photon pulse emitted from the NV center in diamond based on our experimental results in the previous section. Here we estimate the well-known intensity correlation $g_0^{(2)}$ of the converted light pulse to see the ability of the frequency down-converter to preserve the non-classical property $g_0^{(2)}<1$. We regard a part of the optical circuit including the PPLN and the two BGs as an essential part of the converter, which is the region surrounded by dashed lines in Fig. 1. In the following, we derive the intensity correlation and the average photon number of a converted telecom light pulse from the converter when those of a 637 nm signal light pulse are given.

Let us first derive the intensity correlation of a light pulse X which is a mixture of two statistically-independent light pulses A and B with the intensity correlation $g_{0,\text{A}}^{(2)}$ and $g_{0,\text{B}}^{(2)}$ and the average photon number 〈n̂_A〉 and 〈n̂_B〉, where n̂_A(B) represents the photon number operator. The intensity correlation of each pulse is given by $g_{0,i}^{(2)}=〈{\widehat{n}}_i({\widehat{n}}_i-1)〉/{〈{\widehat{n}}_i〉}^2$ for i = A, B, X. We also define the Fano factor F_i = 〈(Δn̂_i)²〉/〈n̂_i〉, where Δn̂_i = n̂_i − 〈n̂_i〉. We then obtain $〈{\widehat{n}}_i〉\left(g_{0,i}^{(2)}-1\right)=\left(〈{\widehat{n}}_i^2-{\widehat{n}}_i〉-{〈{\widehat{n}}_i〉}^2\right)/〈{\widehat{n}}_i〉=〈{\left(\mathrm{\Delta }{\widehat{n}}_i\right)}^2〉/〈{\widehat{n}}_i〉-1=F_i-1$. When the two light pulses A and B are statistically independent so that 〈Δn_AΔn_B〉 = 0, the Fano factor of the light pulse X is calculated to be F_X = 〈(Δn̂_A + Δn̂_B)〉²/〈n̂_A + n̂_B〉 = F_A〈n̂_A〉/〈n̂_A + n̂_B〉 + F_B〈n̂_B〉/〈n̂_A + n̂_B〉. As a result, the intensity correlation of the light pulse X is given by

Suppose that the intensity correlation of a 637 nm input light pulse is $g_{0,\text{in}}^{(2)}$ and the average photon number of the light is n̄_in,sig. For simplicity, we assume that the spectral width of the input light is much narrower than the phase-matching bandwidth ≈ 0.1 nm of the frequency down-converter. We also assume that the background photons induced by the pump light follow the Poisson statistics, and are independent of the down-converted photons. It is convenient to replace these background photons by a noise source placed at the input of the down-converter. The average photon number n̄_in,noise of this equivalent input noise is then given by n̄_in,noise = BPΔ_filτ_time/(T_inη_convT_ocT_attε). Here τ_time is a measurement time window, and Δ_fil is a ratio of a filter bandwidth to the bandwidth of Δ̃ ≈ 0.7 nm in the current experiment. Note that we assume that the bandwidth of the filter is much wider than the spectral width of the 637 nm signal light. The reason why the component of the background photons is proportional to τ_time and Δ_fil is that the background photons induced by the cw pump light for the wavelength conversion are temporally continuous and spectrally broad. From the observed values in the previous section as B ≈ 135 Hz/mW, T_in ≈ 0.88, T_oc ≈ 0.31, T_att ≈ 0.083, ε ≈ 0.6 and ${\eta }_{\text{conv}}={\eta }_{\text{conv}}^{\text{max}}{\text{sin}}^2(\sqrt{\kappa P})$ with ${\eta }_{\text{conv}}^{\text{max}}\approx 0.44$ and κ ≈ 5.8/W, we calculate as ${\overline{n}}_{\text{in},\text{noise}}\approx 2.2\times {10}^4{\mathrm{\Delta }}_{\text{fil}}{\tau }_{\text{time}}P/{\text{sin}}^2(\sqrt{5.8P/\text{W}})$. By substituting ( $g_{0,\text{A}}^{(2)},〈{\widehat{n}}_{\text{A}}〉$) and ( $g_{0,\text{B}}^{(2)},〈{\widehat{n}}_{\text{B}}〉$) in Eq. (2) by ( $g_{0,\text{in}}^{(2)},{\overline{n}}_{\text{in},\text{sig}}$) and (1, n̄_in,noise), respectively, and by using ζ_in = n̄_in,sig/n̄_in,noise, the intensity correlation $g_{0,\text{out}}^{(2)}$ of the output light pulse is given by

Below we borrow the observed value of $g_{0,\text{in}}^{(2)}\approx 0.16$ and a lifetime of τ ≈ 13.7 ns for the 637 nm light pulse from the NV center in the diamond nanocrystal reported in [23], and then we estimate the expected value of $g_{0,\text{out}}^{(2)}$ for the converted telecom light. We assume that the spectral width of the 637 nm light is close to the transform-limit so that it is much narrower than Δ_filΔ̃. We choose τ_time = 52ns to collect the pulsed signal light over 99%, and use P ≈ 0.43 W which achieves the maximum conversion efficiency in our experiment. From Eq. (3) and $g_{0,\text{in}}^{(2)}\approx 0.16$, we can calculate $g_{0,\text{out}}^{(2)}$ which is shown as a function of Δ_fil for n̄_in,sig = 10⁻³, 10⁻², 10⁻¹, 1 in Fig. 4. As a reference, we also show $g_{0,\text{out}}^{(2)}$ for the converted telecom light when the 637 nm signal light has $g_{0,\text{in}}^{(2)}=0$ and the same lifetime.

 

Fig. 4 The estimated $g_{0,\text{out}}^{(2)}$ of the converted telecom light as a function of Δ_fil in the cases of $g_{0,\text{in}}^{(2)}\approx 0.16$ (solid curves) and $g_{0,\text{in}}^{(2)}=0$ (dotted curves). The measurement time is fixed to be τ_time = 52ns. The four curves show the intensity correlation in the cases of n̄_in,sig = 1, 10⁻¹, 10⁻² and 10⁻³ from the bottom.

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In practice, the apparent intensity correlation of the light measured by the Hanbury-Brown and Twiss setup [31] is affected by the dark count of the detectors. We assume that coupling efficiencies to the single-mode fibers and two photon detectors for the Hanbury-Brown and Twiss setup are the same as those used in our experiment, namely the transmittance of the optical circuit after the PPLN is T_oc ≈ 0.31, the quantum efficiency is ε ≈ 0.6, and the dark count rate is d = 220 Hz. When a half BS is used for the measurement of $g_{0,\text{out}}^{(2)}$, an expected observed value of $g_{0,\text{out}}^{(2)}$ for the converted telecom light as a function of Δ_fil is shown in Fig. 5(a). From the figure, even for n̄_in,sig = 10⁻³, we see a non-classical intensity correlation $g_{0,\text{out}}^{(2)}\approx 0.77$ of the converted telecom light at Δ_fil = 1.2 × 10⁻³ which corresponds to about 100 MHz. Using Eq. (2), we also calculate an expected SNR of the converted telecom light at the each detector under the assumption that the 637 nm light is a mixture of two statistically-independent light sources composed of an ideal single photon and background photons that follow the Poisson statistics, and show the results in Fig. 5(b). We believe that the intensity correlation of the background photons is close to 1 because the observed cw background photons should spread in multiple modes even for the filter with Δ_fil = 1.2 × 10⁻³. We note that $g_{0,\text{out}}^{(2)}$ is linearly dependent on the intensity correlation of the background photons from Eq. (2). For example, if the background photons had the intensity correlation of 1.5, the expected observed intensity correlation of the converted telecom light would be $g_{0,\text{out}}^{(2)}\approx 0.88$.

 

Fig. 5 The expected observed values of $g_{0,\text{out}}^{(2)}$ and SNR of the converted telecom light when we perform the Hanbury-Brown and Twiss experiment as a function of Δ_fil in the cases of $g_{0,\text{in}}^{(2)}\approx 0.16$ (solid curves) and $g_{0,\text{in}}^{(2)}=0$ (dotted curves). The measurement time is fixed to be τ_time = 52ns. (a) The four curves show the intensity correlation in the cases of n̄_in,sig = 1, 10⁻¹, 10⁻² and 10⁻³ from the bottom. (b) The four curves show the SNR in the cases of n̄_in,sig = 1, 10⁻¹, 10⁻² and 10⁻³ from the top.

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In the above estimation, we assumed the spectral bandwidth of the 637 nm signal light is much smaller than the phase-matching bandwidth ≈ 0.1 nm of PPLN crystal and the filter bandwidth Δ_filΔ̃, where Δ̃ ≈ 0.7 nm, while it was not satisfied in the experiment reported in [23] due to the inhomogeneous broadening at the room temperature. Such a transform-limited narrow bandwidth light pulse from the zero phonon line of a NV center in a bulk diamond at a low temperature has been reported in [20,26]. In [26], n̄_in,sig = 4 × 10⁻⁴ was reported, and the low preparation probability of the light leads to the expected value of $g_{0,\text{out}}^{(2)}$ as ≈ 0.92 for Δ_fil = 1.2 × 10⁻³. In recent years, there are several studies for efficient collection of the light from NV center using a solid immersion lens [21, 22] and a photonic crystal cavity [32]. When such experimental efforts will meet our requirements of the 637 nm signal light in the near future, the demonstrated low noise frequency down converter will clearly achieve the conversion of the non-classical light from the NV centers to the telecom band.

4. Conclusion

In conclusion, we have demonstrated that the low noise frequency down-conversion of the photon at 637 nm which corresponds to a resonant wavelength of the NV center in diamond to the telecommunication band. The analysis based on our experimental results shows that if the transform-limited light pulse from the NV center in diamond is prepared even with a probability of 10⁻³, the intensity correlation of the telecom light after the frequency down-conversion with the proper frequency filtering will be well below 1. We believe that the result will lead to the efficient connection between solid-state devices composed of the NV center in diamond and telecom fiber networks.