We report the generation of high-purity correlated photon-pairs and polarization entanglement in a 1.5 μm telecommunication wavelength-band using cascaded χ(2):χ(2) processes, second-harmonic generation (SHG) and the following spontaneous parametric down conversion (SPDC), in a periodically poled LiNbO3 (PPLN) ridge-waveguide device. By using a PPLN module with 600%/W of the SHG efficiency, we have achieved a coincidence-to-accidental ratio (CAR) higher than 4000 at 7.45×10−5 of the mean number of the photon-pair per pulse. We also demonstrated that the maximum reach of the CAR was truly dark-count-limited by the single-photon detectors used here. This indicates that the fake (noise) photons were negligibly small in this system, even though the photon-pairs, the Raman noise photons, and the pump photons were in the same wavelength band. Polarization entangled photon pairs were also generated by constructing a Sagnac-loop-type interferometer which included the PPLN module and an optical phase-difference compensator to observe maximum entanglement. We achieved two-photon interference visibilities of 99.6% in the H/V basis and 98.7% in the diagonal basis. The peak coincidence count rate was approximately 50 counts per second at 10−3 of the mean number of the photon-pair per pulse.
© 2011 OSA
Parametric fluorescence by spontaneous parametric down conversion (SPDC) in second-order optical nonlinear materials and spontaneous four-wave mixing (SFWM) in third-order optical nonlinear materials is a key element of quantum-correlated, and entangled, photon-pair sources to realize various quantum information and communication technologies (QICTs) such as quantum cryptography  and computing . Waveguide based parametric fluorescence source is very attractive for its compactness and high conversion efficiency. Preceding works on the generation of polarization entangled photon-pairs based on waveguide sources were completely reviewed in . The waveguide sources of the polarization entangled photon-pairs have achieved net visibilities greater than 90%.
In particular, the SPDC process is a three-photon process where a pump photon is split into a signal and idler photons via the second-order optical nonlinearity (χ(2)) of a nonlinear optical material. SPDC has been well studied and is a common process in various χ(2) materials. While the SPDC process is in general more effective in comparison with the SFWM process in χ (3) material, it often requires a complicated optical coupling system. This is because the photons at quite different wavelengths (short-wavelength pump photon and long-wavelength photon-pair) should often coexist in their optical paths [4–6]. This is quite different from the case of a single wavelength-band system based on the SFWM [7–10] where both the pump photon and the generated photon-pair are in the same wavelength-band.
Cascaded χ(2) processes have been well known and studied, especially for broad-band wavelength-conversion in conventional (classical) large-capacity optical communication applications [11,12]. This process is achieved by second harmonic generation (SHG) and the following differential-frequency generation (DFG) in a single χ(2) material, named as cascaded SHG/DFG (c-SHG/DFG). While the cascaded χ(2) process mimics the FWM process in a pure χ (3) material, the efficiency is much greater than that of a pure χ (3) system. The quasi FWM efficiency in periodically poled LiNbO3 (PPLN) under a quasi-phase-matching (QPM) condition is known to be 104-105 times larger than that of pure χ (3) process such as in a silica glass .
Considering the physical similarity between the c-SHG/DFG process and the cascaded SHG/SPDC (c-SHG/SPDC) process, we can expect the c-SHG/SPDC-based system to be a powerful and promising candidate as an entangled photon-pair source which is more efficient and compact than the SFWM-based one.
In addition, this new approach of the c-SHG/SPDC process can be achieved only by using optical resources (lasers, filters, and the others) at a single wavelength-band, just like the SFWM-based system. This indicates that the entangled photon-pair source at fiber-optic telecommunication wavelengths (1.5-μm or 1.3-μm band) can be achieved by entirely using optical resources in the single wavelength band. Considering the robustness, low-cost, and excellent performance of the optical resources for fiber-optics telecommunication applications, this feature of the c-SHG/SPDC system is quite interesting and has great impact to the applications upon deployment.
Ideas similar to our c-SHG/SPDC realization have been previously reported in the generation of squeezed vacuum and time-bin entanglement [13,14]. Hunault et al. have reported a time-bin entangled photon-pair source based on the c-SHG/SPDC . They have reported a coincidence-to-accidental ratio (CAR) of 300 and visibilities greater than 94% by using a PPLN device with 60%/W of the SHG efficiency. In a slightly different way, Jiang and Tomita have also reported the generation of polarization-entangled photon-pairs by cascading two PPLNs in a single chip of PPLN device . In this method the SHG and the SPDC are independently generated in each section of the cascaded PPLNs and each function is definitely separated.
In this paper, we report the generation of high-purity correlated photon-pairs and polarization entanglement in a 1.5 μm telecommunication wavelength-band using a c-SHG/SPDC process in a periodically poled LiNbO3 (PPLN) ridge-waveguide device. The single and coincidence counts were investigated in detail by using ultra-low-noise single-photon detectors based on sinusoidally gated InGaAs/InP avalanche photodiodes (SG-APDs) [16,17]. By using a PPLN module with 600%/W of the SHG efficiency, we achieved a high CAR value larger than 4000 at 7.45×10−5 of the mean number of photon-pairs per pulse. This value was actually limited by the dark counts of the SG-APDs, and not dominated by the coexistence of fake (noise) photons such as spontaneous Raman scattering, even though the photon-pair, the Raman-induced noise photons, and the pump photons were in the same wavelength-band. This indicates that the approach using the c-SHG/SPDC process is a promising candidate as a simple and low-cost high-purity photon-pair source with negligible noise photons. Polarization entanglement was also successfully achieved by using Sagnac loop configuration which included the PPLN device. We observed clear two-photon interference fringes with visibilities of 99.6% in the H/V basis and 98.7% in the diagonal basis, respectively. The peak coincidence count rate was approximately 50 counts per second at 10−3 of the mean number of the photon-pair per pulse.
2. Operation principle
Figure 1 schematically illustrates (a) the c-SHG/SPDC process used here and (b) the standard (single-stage) SPDC process. In the standard SPDC process a pump photon is directly split into a pair of photons (signal and idler photons) in a χ(2) material such as the PPLN device. To satisfy energy conservation, the wavelength of the pump photon should be quite different from that of the SPDC photons, typically about half of the wavelengths of the SPDC photons, in the standard SPDC process (Fig. 1 (b)).
In the c-SHG/SPDC process used here, in contrast, an external pump light first excites second-harmonic generation (SHG) inside the PPLN device, and then the second-harmonic (SH) photon is down-converted into a photon pair through the following SPDC process via another χ(2) process in the same PPLN device (Fig. 1 (a)). According to this process, a short-wavelength pump-photon, which should be a seed of the SPDC process, can be also created inside the PPLN device without an external short-wavelength pump light. Since the SH photon is needed only inside the PPLN device, this photon-pair source never needs optical coupling of the short-wavelength lights into and out of the PPLN device.
The energy-conservation law for each process (SHG and SPDC) is given by
where ω is the optical angular frequency.
The quasi-phase-matching (QPM) conditions for the SHG process and the SPDC process are respectively given by
where k is the wave number, and K corresponds to the period of spatial modulation of χ(2) coefficient for the QPM. Notations p, s, i denote pump, signal, and idler photons, respectively.
Equations (2) and (3) cannot generally coexist. But as long as the refractive-index dispersion around the pump, the signal, and the idler wavelengths yields a linear relationship, i. e., the refractive index n is simply given by , thus can be satisfied and therefore the two equations can coexist. Within this wavelength region, the SPDC process can efficiently occur in the same PPLN device, simultaneously satisfying the QPM condition for the SHG process.
The c-SHG/SPDC process has different spectral properties from those of the standard SPDC. Figure 2(a) shows typical SPDC spectra under the QPM conditions of the standard SPDC process (black curve) and of the c-SHG/SPDC process (red curve) in a PPLN device. The PPLN device used here was the home-made PPLN device described in Section 3. In these experiments continuous-wave (CW) light was used as the pump light. The horizontal axis represents the wavelength detuning from the pump wavelength. The c-SHG/SPDC process typically showed broader SPDC spectra than the standard SPDC process. In this case the 3-dB bandwidth (at half-width half-maximum) of the standard SPDC was estimated to be approximately 27 nm, and it was approximately 36 nm for the c-SHG/SPDC.
The difference between the standard and cascaded processes also appeared in their tolerance to phase mismatching. Figure 2(b) shows the changes of the SPDC intensities when the pump wavelength was changed. Here the horizontal scale is the detuning of the pump wavelength from the QPM wavelength (in the case of the standard SPDC the detuning was defined as difference between twice the pump wavelength and the QPM wavelength). The SPDC intensities were measured at 10 nm wavelength offset from the pump wavelength. The SPDC intensity in the c-SHG/SPDC process was kept in a wider pump-wavelength detuning range, compared to the standard SPDC case. The 3-dB bandwidth, which was defined as the pump-wavelength detuning when the SPDC intensity was reduced by 3 dB from its peak value, was estimated to be 0.14 nm for the standard SPDC and 0.24 nm for the c-SHG/SPDC.
These results indicate that the c-SHG/SPDC process is more tolerant to a mismatching of the pump wavelength than the standard SPDC. This also means that the system is tolerant to the mismatching of the operating temperature. This feature of the c-SHG/SPDC process should be welcome for practical applications.
3. Photon-pair generation
Figure 3 shows the experimental setup for the correlated photon-pair generation via c-SHG/SPDC process. The home-made PPLN device used here was a MgO-doped, LiNbO3 ridge-waveguide device . Details of the device fabrication can be referred to . Type-0 QPM using d33 coefficient of the second-order optical nonlinearity was used. After fabricating the periodic domain inversion on z-cut LiNbO3 substrate using an electrical poling method to achieve the QPM condition, an annealed proton exchanged layer was first formed on top of the PPLN substrate for optical confinement mainly in the vertical direction. After that a ridge waveguide was formed using a dicing saw for the optical confinement in the horizontal direction. The width of the ridge waveguide was approximately 10 μm.
The period of the domain inversion was 19.0 μm, corresponding to approximately 1548.6 nm of the QPM wavelength at 31.6 °C in this work.
The PPLN device was then packaged in a fiber-pigtailed optical module with a thermistor, a thermoelectric cooler, and two polarization-maintaining optical fibers (PMFs) for standard telecommunication uses. The device length was 60 mm in this work. The insertion loss of the module was estimated to be approximately 3.0 dB at the 1.5-μm band, including coupling losses to the pigtail fibers and transmission loss of the PPLN waveguide.
The SHG conversion efficiency was estimated to be approximately 600%/W under the QPM condition. The 3-dB bandwidth of the SHG curve was approximately 0.16 nm in terms of the pump wavelength. The temperature shift of the QPM wavelength was approximately +0.15 nm/K.
The pump pulses were generated using a wavelength-tunable external-cavity laser diode and a semiconductor electroabsorption (EA) modulator. The pulse repetition rate, the pulse width, and the center wavelength of the pump pulses were 1 GHz, 60 ps, and 1548.66 nm (corresponding to the QPM wavelength), respectively. After amplification by a polarization-maintaining erbium-doped fiber amplifier (PM-EDFA), residual amplified spontaneous emission (ASE) was first eliminated by an optical bandpass filter (OBF#1). And then the pump pulses were input to the PPLN module. After the PPLN module, an optical low pass filter (LPF) and two WDM filters (WDM#1 and WDM#2) were first used to eliminate the pump light and the SHG light. Then the signal/idler photons were separated using WDM#3 and two optical bandpass filters (OBF#2 and OBF#3).
Figure 4 shows the total transmittance characteristics of the optical filters after the PPLN module. In this work we set the center wavelengths of the signal photons and the idler photons to 1538.8 nm and 1558.66 nm, respectively. Wavelength detuning from the pump wavelength was approximately 10 nm. The peak transmittance was −5.7 dB for the signal photons and −4.8 dB for the idler photons. The 3-dB bandwidths of the transmittance window were 0.78 nm for the signal photons and 0.86 nm for the idler photons, respectively. The pump suppression ratio at 1548.66 nm was greater than 130 dB. This value was enough to suppress residual pump photons to the levels much lower than dark count levels of the photon detectors.
The signal/idler photons were then photon-counted using the SG-APDs (D1, D2) [16,17]. Two detectors were synchronized to the pump pulses and the detection rate was 1 GHz. The detection efficiencies of both the APDs were estimated to be approximately 8%. The dark counts were approximately 1040 counts/s for the signal channel and 440 counts/s for the idler channel, respectively. The coincidence events were measured by a time-interval analyzer (time resolution = 39.0625 ps). In our experimental setup, the coincidence counts were integrated till total amount of the start signals reached a preset value. The preset value was set at 3×106. The acquisition time depends on the count rate of the start signals, i. e., signal count rate, and it becomes longer as the mean number of the photon-pair decreases.
Figure 5 shows dependence of (a) the single count rates per pulse of the signal photons (black circles) and the idler photons (red squares) and (b) the coincidence count rate per pulse (black circles) on the averaged power of the pump pulses. In Fig. 5(b), the accidental count rates at unmatched time slot were also shown as red open squares. All data included the dark counts of the APDs. 0 dBm of the averaged pump power approximately corresponded to 11.7 dBm of the pulse peak power in our experimental conditions.
The single count rates and the coincidence count rate had quadratic dependence on the pump power, agreeing well with the theoretical prediction. In contrast, the accidental count rate had power dependence of P4 (P: pump power). This indicates that the accidental counts were mainly dominated by counting of the SPDC photons at different time slots. This also implies that the linear optical process such as the spontaneous Raman scattering (spRS) was not dominant effect to the accidental counts. This suggests that the amount of noise photons was very small in this c-SHG/SPDC system.
The coincidence-to-accidental ratio (CAR) is known to be a powerful tool to estimate how many undesired noise photons are generated together with the needed correlated photon-pairs . The CAR is defined as 
where cs and ci are the single count rates per pulse for the signal photons and the idler photons, Rm is the coincidence count rate at the matched time slot, and Rum is the coincidence count rate at the mismatched time slot (corresponding to accidental count rate). μc, μxn, αx and dx are the mean number of correlated photon-pairs per pulse, the mean number of noise photons per pulse for channel x, the transmittance for channel x, and the dark count rate for channel x, with x = s (signal) or i (idler), respectively.
In our case of the c-SHG/SPDC, μc has quadratic dependence on the pump power (P), whereas the noise photons (μxn) represented by the spRS is linearly proportional to the P. Therefore at a high pump level the dark counts and the noise photons can be relatively neglected in comparison with the correlated photons. At such high pump levels, be satisfied. From this relationship, the total transmittance (αx) were estimated to be approximately −19.8 dB for the signal channel and −18.9 dB for the idler channel, respectively, including the transmission and coupling losses of the PPLN module, transmittance of the optical filters, and the detection efficiencies of the APDs.
Figure 6 (a) shows dependence of the CAR on the mean number of photon-pair per pulse. Figures 6 (b) also show time-correlation histogram measured in the time-interval analyzer when the mean number of the photon-pair was 7.45×10−5. In this case the signal count rate was approximately 1850 counts per second, and the acquisition time of the coincidence counts was approximately 3×106/1850 ~27 minutes.
The measured CAR first monotonically increased as the mean number of the photon-pair decreased, as expected theoretically. Then the CAR reached the maximum value limited by the dark counts of the detectors (dx) as well as the uncorrelated noise photons (μxn).
The maximum reach of the CAR was 4138 at 7.45×10−5 of the mean number of the photon-pair in this study. This value was comparable to the best value of the CAR ever reported, 4452, which was achieved in the standard-SPDC-based system and superconductive single photon detectors (SSPDs) .
When we compared the performances of the c-SHG/SPDC system with the other single wavelength-band systems using the SFWM, the merit of the c-SHG/SPDC system was further clarified. The CAR using the SFWM in optical fiber is typically much less than 100 at room temperature [19,21]. The CAR barely reaches over 1000 by cooling the fiber to liquid helium temperature . The maximum CAR was still limited to approximately 200 even though silicon nanowire, which had very high optical nonlinearity due to very small mode-field diameter, was used as the SFWM source .
The high CAR value of the c-SHG/SPDC is partly due to low dark counts and low after-pulse probabilities of the SG-APD-based detection systems , but substantially originates from low noise photons in the c-SHG/SPDC-based photon-pair generation.
Red, blue, and green curves in Fig. 6(a) are the calculation results of the CAR when we neglect the noise photons and consider only the dark counts of the APDs as noise source. The experimental results (black circles) were in good agreement with the calculation results.
Neglecting the noise photons (μxn = 0), the maximum reach of the CAR limited by the dark counts of the detectors is given by
In this study the dark count rates (ds and di) were approximately 1.04×10−6 ns−1 and 4.4×10−7 ns−1, respectively. The dark count rates fluctuated by over 1×10−7 during the experiments. The losses (αs and αi) were estimated to be −19.8 dB and −18.9 dB, respectively. From these values, using Eq. (9), the maximum reach of the CAR was calculated to be approximately 4000. This value was in good agreement with the experimental result. This verifies negligibly small noise photons of the c-SHG/SPDC-based system and indicates that the c-SHG/SPDC can provide noise-photon-free, high-purity photon-pairs for quantum entangled light sources.
4. Polarization entanglement
We demonstrated polarization entanglement experiments using the c-SHG/SPDC photon-pair source mentioned above. The experimental setup was shown in Fig. 7 . The polarization entanglement was achieved using conventional Sagnac loop configuration with polarization beam splitter/combiner (PBSC) . All the setup consisted of polarization-maintaining-fiber (PMF)-pigtailed optical components for standard telecommunication uses. No special optical components, for example, the PBSC operating both at short and long wavelengths, were needed in this system. This verifies the merit of the c-SHG/SPDC-based system considering practical uses. The PM pigtail fibers of the optical modules were 90°-spliced at the center position to compensate for the birefringence of the PMFs.
45°-polarized pump pulse was split into horizontal (H) and vertical (V) polarization components at the PBSC, and then two pump pulses propagated in the loop in the counter-clockwise (CCW) and clockwise (CW) directions, respectively. The signal and the idler photons by the c-SHG/SPDC from the fiber loop then passed the optical filtering system as same as that in the earlier section. Then the coincidence counts were measured by the SG-APDs. Polarization controllers consisting of λ/2 wave plate and λ/4 wave plate were installed before the photon detectors (D1 and D2) in order to compensate polarization rotation originating in misalignment of the optical axes of the PMF-pigtailed optical components.
The optical phase bias compensator (OPBC) shown in Fig. 8 was installed in the fiber loop in order to compensate the optical phase difference between two biphoton states, and .
The OPBC consisted of two Faraday rotators and a quartz Babinet-Soleil compensator (BSC) located between the Faraday rotators (see Fig. 8) . As is obvious from the geometric configuration of the OPBC, when S-polarized light propagating in the right direction inputs to the OPBC, the light propagates in the BSC as X-polarized light. Then it outputs as P-polarized light, orthogonal polarization to the initial (S) polarization, from the OPBC. In contrast, when P-polarized light propagating in the left direction inputs to the OPBC, it outputs as S-polarized light from the OPBC, propagating as Y-polarized light (orthogonal to X-polarization) in the BSC. As a result, the two counterpropagating lights undergo orthogonal polarization states only at the BSC. This implies that the two lights undergo a phase difference only given by the BSC.
As shown in Fig. 8, when the pump, signal, and idler photons pass the OPBC, their polarization is rotated by 90 °. Therefore two counterpropagating pump pulses are bidirectional coupled to the PPLN in the same polarization (H polarization) although they have H and V polarization initially at the output of the PBSC. When the SPDC photon-pairs propagating in the CCW direction pass the OPBC, their polarization is also rotated by 90° and it is changed to V polarization. As a result polarization entanglement is achieved in this setup.
When the OPBC is included in the optical loop we can give any optical phase difference between and states. This implies that two maximally entangled states, , can be freely generated by adjusting the optical phase of the OPBC so as to compensate the optical phase difference due to residual birefringent of the PMF-pigtailed optical components and the difference of the optical path lengths.
We fixed the polarizer angle of the signal polarizer (θs), and measured the coincidence count rates while rotating the polarizer angle of the idler polarizer (θi). The averaged pump power coupled to the PPLN module was approximately −6.5 dBm. The mean number of the photon-pair per pulse was estimated to be approximately 0.001. A preset value of total amount of the start signals was set at 6×105 in these experiments. The signal count rate was approximately 7800 counts per second, and the acquisition time of the coincidence counts was approximately 6×105/7800 ~77 seconds.
Figures 9 show the coincidence rates per start (signal) pulses as a function of θi at the H/V basis and the diagonal basis (θs = 0° and 45 °, respectively). The optical phase difference in the OPBC was adjusted so that the coincidence counts were minimized when θs = 45° and θi = −45 °. This phase was held constant during the experiments. All the data were raw data without subtracting accidental counts.
Clear two-photon interference fringes were measured. The interference fringes were well fitted with curves (solid curves in Fig. 9), indicating that was realized in these experiments. The visibilities of the fitted curves were estimated to be 99.6% in the H/V basis (θs = 0 °) and 98.7% in the diagonal basis (θs = 45 °), respectively. These results verified the successful generation of high-purity polarization-entangled photon pairs using the c-SHG/SPDC. The peak coincidence counts were estimated to be 4050 ± 150 counts in the H/V basis and 3722 ± 190 counts in the diagonal basis, whereas the minimum coincidence counts were 9.8 ± 2.4 counts (H/V basis) and 28 ± 7.1 counts (diagonal basis), respectively. The peak coincidence count rate was estimated to be approximately 50 counts per second in this experimental condition. Slight difference in the peak coincidence rates was mainly due to polarization-dependent loss (PDL). This was coming from the insertion loss of the OPBC module and the PDL of each optical module. This will be improved by further refining the setup of the optical system.
Considering the state of the art of the related technologies, we can expect further improvement on the efficiency and the quality of the entangled photon-pairs. Highly effective PPLN devices with the SHG conversion efficiencies greater than several thousand %/W have been reported in some literatures [24–26]. Use of such highly effective PPLN device will lead to a more compact and cost-effective entangled photon-pair source which is directly pumped by a semiconductor laser without any optical amplifiers. High conversion efficiency will also further reduce the Raman-induced noise photons. This leads to further improvement on the purity of the generated photon-pairs.
In summary we have successfully achieved the generation of high-purity correlated photon pairs and polarization entanglement in the 1.5 μm wavelength-band using the c-SHG/SPDC in a PPLN ridge-waveguide device. By using a PPLN module with 600%/W of the SHG efficiency, we obtained a high CAR value larger than 4000. We have shown that the maximum reach of the CAR was truly limited by the dark counts of the single-photon detectors and that noise photons such as spRS photons were not a dominant factor to limit the CAR. This indicates that noise photons could become negligibly small in the c-SHG/SPDC system, even though the photon-pair, the Raman noise photons, and the pump photons were in the same wavelength-band. The experimental results verified advantage of the c-SHG/SPDC system as a high-purity photon-pair source with negligibly small noise photons. The polarization entanglement has been also successfully achieved. We obtained high visibilities in the two-photon interference fringes of 99.6% in the H/V basis and 98.7% in the diagonal basis, respectively. These results indicate that the c-SHG/SPDC-based system can provide noise-photon-free, high-purity photon-pair and entanglement light source for quantum information and communication technologies.
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