1. Introduction

Quantum entanglement is peculiar to quantum mechanics, which is not explained by the laws of classical physics. A promising application of quantum entanglement in real communication networks is quantum key distribution (QKD) over optical fiber links [1, 2] or in free-space [3, 4] for confidential communications.

An entangled photon-pair source based on spontaneous parametric fluorescence (SPF) in a nonlinear optical medium [5–10] is one of the most practical types for real applications. SPF-based photon-pair sources using spontaneous parametric down-conversion (SPDC) in a second-order nonlinear optical medium [5–8] and spontaneous four-wave mixing (SFWM) in a third-order nonlinear optical medium [9, 10] have been reported. The SPF-based photon-pair source has been used in many experimental studies concerning quantum information and communication technologies.

SPF-based photon-pair sources generally have a broad spectral bandwidth. The SPF bandwidth typically occupies several tens of nanometers in the 1.5-μm wavelength band [11]. Such spectral broadness often hinders the generation of indistinguishable photon pairs, and it interferes with some applications such as quantum repeaters [12]. However, this feature becomes, from another point of view, an attractive advantage for wavelength-multiplexed entanglement distribution, which enables multi-user applications [13].

When the broad spectra of SPF-based entanglement sources are spectrally spliced, a specific pair of wavelength channels that satisfies the energy conservation law can always share deterministic correlation results, whereas unmatched pairs merely share probabilistic results. This can be applied to a QKD system delivered to multiple users, in which many user pairs can share different secret keys simultaneously and one shared key for one user-pair has no correlation with the other shared keys for different user pairs, maintaining security for every user. These features of wavelength-multiplexed entanglement distribution will provide more flexible and usable QKD systems in future networks.

We can prepare a broad band entanglement source for wavelength-multiplexed QKD system using SPDC directly [13] with, for example, a tunable Ti: sapphire laser. When we consider, however, realizing the wavelength-multiplexed QKD systems most reliably and cost-effectively for real applications in communication systems, system construction using existing optical telecommunication infrastructure and optical resources that are standard in the telecom field is desirable. We recently reported an entangled photon-pair source by using cascaded χ ⁽²⁾ processes, second–harmonic generation (SHG), and subsequent SPDC (c-SHG/SPDC process) [11]. We revealed that this photon-pair source could provide high-purity photon pairs entirely by using optical resources that are standard in the telecom field [11].

However, a highly intense pump light is always located at the center of the SPDC spectra in the c-SHG/SPDC method. Therefore, a large amount of the spectral component (>10 nm) must be discarded and cannot be used as the QKD channels, even though it is also the best qualified considering that it yields perfect quasi-phase-matching [Fig. 1(a)]. This also means that the generated photon pairs should be highly frequency nondegenerate.

 

Fig. 1 (a) Cascaded SHG/SPDC with single-pump scheme. (b) Cascaded SFG/SPDC with double-pump scheme (this work).

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This drawback of the c-SHG/SPDC system can be resolved by using a double pump scheme [Fig. 1(b)] [14]. In this setup, seed light for the SPDC process is generated through sum-frequency generation (SFG) by the two pump lights. In this new setup, which is quite similar to the concept of the cascaded SFG/differential-frequency generation (DFG) in classical optical communication [15], the wavelengths of the pump lights can be set apart from the main spectral lobe of the SPDC spectra, and the main portion of the SPDC spectra, which is totally degenerate, can be freely used as the QKD channels.

In this paper, we report the generation of nearly degenerate, wavelength-multiplexed polarization-entangled photon pairs by using cascaded SFG/SPDC with the double pump scheme in a periodically poled LiNbO₃ (PPLN) ridge waveguide device. We observed clear two-photon interference fringes with visibilities higher than 98% for all the evaluated wavelength channels (eight pairs) in this study. We also performed a detailed experimental investigation of the cross-talk characteristics and detuning characteristics of the pump wavelengths.

2. Experimental setup

Figure 2 schematically depicts the experimental setup. The setup of the polarization-entangled photon-pair source was similar to that in our preceding work [11], except that two pump lights were used in this study. A home-made PPLN device with a ridge waveguide structure was used as a nonlinear optical device. The details of the device structure and the fabrication process of the PPLN are available elsewhere [16]. It showed an SHG conversion efficiency of approximately 600%/W under the quasi-phase-matching (QPM) condition. The PPLN device was then packaged in a fiber-pigtailed optical module with a thermistor, a thermoelectric cooler, and two polarization-maintaining optical fibers for standard telecommunication uses. The insertion loss of the module was estimated to be approximately 5.3 dB in the 1.5-μm band.

 

Fig. 2 Experimental setup of the wavelength-multiplexed polarization entanglement by c-SFG/SPDC in a PPLN device. PBSC: polarization beam splitter/combiner. OPBC: optical phase-bias compensator. PC: polarization controller. AWG: arrayed waveguide grating module. EDFA: Erbium-doped fiber amplifier. LD: laser diode.

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In this work we define the QPM wavelength (λ_QPM) as the pump wavelength at which the conversion efficiency of the SHG is maximized. Here, λ_QPM was 1552.0 nm at a PPLN module operating temperature of 52.0 °C. Throughout this study, the wavelengths of the two pump lights (λ_p1 and λ_p2) for SFG were set so as to satisfy the QPM condition in terms of the SHG, i.e., $1/{\lambda }_{p1}+1/{\lambda }_{p2}=2/{\lambda }_{QPM}$, where λ_QPM was 1552.0 nm. In other words, the wavelength of SFG in the c-SFG/SPDC was always fixed and equal to the optimized wavelength of the SHG in the c-SHG/SPDC process.

One of the pump lights was pulsed light generated by using a wavelength-tunable external-cavity laser diode and a LiNbO₃ intensity modulator. The pulse repetition rate, pulse width, and center wavelength were 240 MHz, 120 ps, and 1542.00 nm, respectively. The other pump light was continuous-wave (CW) light at a wavelength of 1562.13 nm. The wavelength detuning of the pump lights from the QPM wavelength was approximately 10 nm.

The experiments will be possible even when the pump lights are both CW or pulsed. Considering the single-photon detectors used here (InGaAs avalanche photodiodes (APDs) with gated Geiger mode), however, the pulsed pump setup is preferable, because the CW setup generates photon pairs that cannot be detected by the photon detectors, so it is inefficient. Operation is most efficient when the pump lights are both pulsed. In this case, however, the two pump pulses must overlap, and we need a control unit to produce a proper time delay in the pump pulses. In terms of the efficiency and compactness of the system, we think that the setup with one pulsed pump laser and one CW pump laser is the best choice for our applications.

After amplification by a polarization-maintaining erbium-doped fiber amplifier (PM-EDFA), residual amplified spontaneous emission was eliminated by using narrow-band optical bandpass filters (OBFs). The two pump lights were 45°-polarized; they then passed through a wavelength-division multiplexing (WDM) filter (WDM#1), and a polarization beam splitter/combiner (PBSC), and finally pumped the PPLN module bidirectionally. The signal and idler photons produced by c-SFG/SPDC from the fiber loop passed an optical filtering system consisting of an optical low-pass filter (LPF), arrayed waveguide grating (AWG) filter, and additional OBFs. The LPF was used to eliminate the SFG light. The AWG filter used here was a 16-channel, 50-GHz-spacing AWG filter commonly used in standard telecom applications. Eight channels (ch#1–ch#8) in the short-wavelength band corresponded to the signal photons, whereas another eight channels (ch#9–ch#16) in the long-wavelength band corresponded to the idler photons. As a result in this work we generated and evaluated eight pairs of wavelength-multiplexed polarization-entangled photon pairs. Each pair of signal and idler photons was set to satisfy the energy conservation law corresponding to $1/{\lambda }_s+1/{\lambda }_i=1/{\lambda }_{p1}+1/{\lambda }_{p2}$ by adjusting the operation temperature of the AWG filter. Table 1 lists the pair numbers and corresponding AWG filter channel number defined in this work.

Table 1. Definition of pair number and the corresponding channel number of the AWG filter

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Unfortunately, owing mainly to poor pump rejection by WDM #1, the pump light rejection was not sufficient when only WDM #1 and the AWG filter were used in this work. To improve this, additional tunable OBFs were installed after the AWG filter.

The signal/idler photons were passed through polarization controllers and rotatable polarizers to evaluate the two-photon interference fringes and then detected by using InGaAs-APD-based single-photon detectors (Princeton Lightwave benchtop receiver PGA-600HSU) (D1, D2). The two detectors were synchronized to the pump optical pulses; the clock frequency was 40 MHz. The detection efficiencies of both APDs were estimated to be approximately 20%. The gate width was 1 ns. The dark count rates were approximately 2 × 10⁻⁶ per pulse for both detectors.

3. Experimental results

3.1 Comparison with single pump, c-SHG/SPDC scheme

We first investigated the spectral characteristics of c-SFG/SPDC and compared them with those of the single-pumped c-SHG/SPDC scheme. In these experiments, the two pump lights were CW lights, and the spectra were measured using an optical spectrum analyzer.

The red curve in Fig. 3 shows the SPDC spectra generated by the c-SFG/SPDC process studied in this work. The spectral components going above −60 dBm were pump lights because we did not use any optical filters and directly measured the outputs from the PPLN module using the optical spectrum analyzer in these experiments. The two other side peaks at 1522 nm and 1582 nm were the result of DFG between the SHG of one pump light and the other pump light. These side peaks appear apart from main lobe of the SPDC spectra and do not interfere with our application.

 

Fig. 3 Comparison of the SPDC spectra obtained by c-SHG/SPDC process (black dashed curve) and c-SFG/SPDC process (red solid curve). Input pump powers and wavelengths were + 11.5 dBm and 1552.0 nm in c-SHG/SPDC, but + 8.2 dBm and 1542.0nm (pump-1), and + 10.4 dBm and 1562.13 nm (pump-2), respectively, in c-SFG/SPDC.

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Symmetric SPDC spectra appeared and the 3-dB bandwidth (at half-width at half-maximum) was estimated to be approximately 28 nm. The spectral bandwidth corresponded to approximately 70 pairs of wavelength channels for the entangled photon pairs when we considered the use of a standard, 50-GHz-spacing AWG filter. Considering the dead band needed to reject the pump lights (approximately 8 nm in our experiments), however, the available bandwidth was reduced to 20 nm, which corresponds to 50 pairs of wavelength channels.

The black dashed curve in Fig. 3 shows the SPDC spectra generated by the single-pump, c-SHG/SPDC process. The c-SFG/SPDC spectra and the c-SHG/SPDC spectra were almost identical, indicating that the two processes had nearly identical spectral properties. The experimental results indicated that the conversion efficiency of the c-SFG/SPDC process was approximately 1.7 dB lower than that of the c-SHG/SPDC process, although these processes should have the same conversion efficiencies theoretically [15]. We think that the difference came mainly from the small phase mismatch in the SFG process due to relatively large detuning (10 nm) from the QPM wavelength. We also think that the conversion efficiencies of SPDC itself were the same for both the c-SFG/SPDC and c-SHG/SPDC because the two cascaded processes had the same pump wavelength for SPDC process in this work.

A little inefficiency (approximately 1.7 dB) of c-SFG/SPDC, however, will not be a serious issue for real uses. As discussed in following sections, averaged powers of pump lights required to produce photon pairs were a few tens of mW at the most. We can now easily obtain such optical powers by using commercial EDFAs in a 1.5-μm wavelength band and easily cover the inefficiency of c-SFG/SPDC process.

3.2 CAR and cross-talk measurements

The coincidence-to-accidental ratio (CAR) in the time-correlation histogram is a powerful tool for estimating quantitatively how many uncorrelated noise photons are generated together with the needed correlated photon-pairs and how pure the generated photon-pairs are [17]. Next, we measured the distribution of the CARs over the wavelength-multiplexed channels. In these experiments, the two pump lights were 0°-polarized and excited only one polarization states, ${|H〉}_s{|H〉}_i$, in the PPLN module.

Figure 4 show the distribution of the CARs over the pair number of the wavelength-multiplexed channels. We measured them under three different pump powers, i. e., mean numbers of photon pairs. The mean numbers of photon pairs were estimated to be approximately 0.05/pulse (black circles), 0.01/pulse (red triangles), and 0.001/pulse (blue squares), respectively.

 

Fig. 4 Distribution of the CARs over the pair number of the wavelength-multiplexed channels as a function of pump power.

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The CARs exhibited almost identical values regardless of the pair number. This indicates that the efficiency of photon-pair excitation was comparable among all the wavelength-multiplexed channels under investigation. This can be understood by the broad spectral bandwidth of the SPDC (>28 nm). The theoretical values of the CARs estimated from the mean number of photon pairs [11] were approximately 20.9, 98.6, and 700 for mean numbers of photon pairs of 0.05/pulse, 0.01/pulse, and 0.001/pulse, respectively. The experimental results agreed well with the theoretical estimate.

Figure 5 shows the cross-talk characteristics when the channel number of the idler photons was changed while the channel number of the signal photons was fixed at ch#7. The mean number of photon pairs was fixed at 0.001/pulse in these experiments.

 

Fig. 5 Cross-talk characteristics among the wavelength channels of the AWG. Closed circles: coincidence counts at matched time slot. Open triangles: accidental counts at mismatched time slot.

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The coincidence counts were remarkably high only when the channel numbers of the signal and the idler were matched to each other (ch#7 and ch#10, respectively, in this case). When the combination of wavelength channels was unmatched, the coincidence counts were dramatically reduced to levels comparable to the accidental counts (open triangles) at the unmatched time slot in the time correlation histogram. The cross-talk to the adjacent channel was less than −20 dB in this work. This value was limited by the cross-talk characteristics of the AWG used here and could be improved considering recent advances in the device technologies of AWG filters in the telecom field.

3.3 Wavelength-detuning characteristics of pump lights

Next, we measured the detuning characteristics of the pump wavelengths. In the detuning experiments, we changed the wavelengths of the two pump lights so as to keep the initial QPM condition defined in the SHG, i.e., $1/{\lambda }_{p1}+1/{\lambda }_{p2}=2/{\lambda }_{QPM}$ (λ_QPM = 1552.0nm). Therefore, the phase matching condition was maintained throughout the detuning experiments. The pump powers were also kept the same throughout the detuning.

Figure 6 shows the changes in the CAR as a function of the wavelength deviation of pump-2 from the QPM wavelength. We measured the CAR under two different pump powers. The changes in the CAR were negligible when the wavelength detuning was less than 24 nm. The coincidence counts were also nearly unchanged in this range of the wavelength detuning. This indicates that approximately 25 nm of pump wavelength detuning was acceptable for retaining the characteristics of the generated photon pairs almost unchanged. This implies that approximately 40 nm of the bandwidth (20 nm each for signal and idler, considering the dead bands for pump rejection) can be freely used in wavelength-multiplexed QKD systems by using the c-SFG/SPDC-based photon-pair source. The bandwidth corresponded to approximately 50 pairs of wavelength channels. The increase in the CAR with further wavelength detuning implies a decrease in the mean number of photon pairs owing to phase mismatching.

 

Fig. 6 Wavelength detuning dependence of the pump lights. Open symbols: results for pair #1. Closed symbols: results for pair #8. Pump wavelengths were set to satisfy the condition of $1/{\lambda }_{p1}+1/{\lambda }_{p2}=2/{\lambda }_{QPM}$ (λ_QPM = 1552.0nm).

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The tolerance value of the pump wavelength detuning was also comparable to the spectral bandwidth of the SPDC spectra (28 nm in a 3-dB bandwidth, see Fig. 3). This indicated that the conversion efficiency was dominated by almost identical physical mechanisms for both the SFG process and the SPDC process in terms of the tolerance to phase mismatching.

3.4 Wavelength-multiplexed polarization entanglement

We investigated the polarization entanglement performance of the wavelength-multiplexed channels by measuring the two-photon interference fringes. In these experiments, the two pump lights were 45°-polarized so as to excite the PPLN bidirectionally. We fixed the polarizer angle of the signal polarizer (θ_s) and measured the coincidence counts while rotating the polarizer angle of the idler polarizer (θ_i). The averaged pump powers were approximately −2.3 dBm for pump-1 (pulsed) and −0.9 dBm for pump-2 (CW), respectively, per end facet of the PPLN module. This condition almost corresponded to the condition at which the mean number of photon pairs per pulse was 0.01. In terms of the conversion efficiency, it is preferable theoretically that both pump lights have the same peak powers. In this work, however, this condition was not satisfied owing to experimental limitations such as insertion losses of the OBFs and lack of another EDFA for amplifying pump-2.

The optical phase difference in the optical phase-bias compensator (OPBC) [11] of the photon-pair source was adjusted so that the coincidence counts were minimized when θ_s = 45° and θ_i = −45°, implying that the quantum state used here was adjusted to be the $1/\sqrt{2}\left({|H〉}_s{|H〉}_i+{|V〉}_s{|V〉}_i\right)$state. All the data were raw data and included the accidental counts. We undertook several runs of measurements under specific conditions, including those in which the coincidence counts were maximized and minimized, i.e., θ_s = 0° and θ_i = 0° and 90° in the horizontal/vertical (H/V) basis, and θ_s = 45° and θ_i = 45° and −45° in the diagonal basis, to obtain the standard deviation and error bars of the measurements.

Figure 7 show the coincidence counts as a function of θ_i in the H/V basis and diagonal basis (θ_s = 0° and 45°, respectively) for three different pairs of wavelength-multiplexed channels. Clear two-photon interference fringes were measured for all the measured wavelength channels. Figure 8 summarizes the visibilities for all eight wavelength-multiplexed channels under investigation in this work. For all the data, visibilities better than 98% were obtained for both the H/V basis (θ_s = 0°) and the diagonal basis (θ_s = 45°). The visibility agreed well with the theoretical prediction (98.8%) from the mean number of photon pairs [18]. This indicates that the photon pairs were highly pure, with no additional noise photons such as those from Raman scattering.

 

Fig. 7 Typical two-photon interference fringes for different pair number. (a) Pair #1. (b) Pair #4. (c) Pair #8. Black closed circles: results for H/V basis. Red closed circles: results for diagonal basis. Polarizer angle of the signal polarizer (θ_s) was 0° (H/V basis) and 45° (diagonal basis), respectively. Solid curves are fitting curves assuming${\cos }^2\left({\theta }_s-{\theta }_i\right)$.

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Fig. 8 Distribution of the visibilities in the two-photon interference fringes over the pair number of the wavelength-multiplexed channels. Black closed circles: results for H/V basis. Red closed circles: results for diagonal basis.

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Figure 9 summarizes the peak coincidence counts. The peak coincidence counts (closed circles) decreased as the pair number increased in this work. However, this was explained well by the changes in the filtering losses (open triangles), implying that the difference did not originate from the photon-pair source itself. This variation in the filtering loss was due mainly to the loss characteristics of the AWG filter used here. The state of the art of AWG technology in standard telecom uses can provide an AWG with more flattened loss characteristics, and a wavelength-multiplexed QKD system with identical system performance for every user is expected.

 

Fig. 9 Summary of the peak coincidence counts over the pair number. Black closed circles: peak coincidence counts for H/V basis. Red closed circles: peak coincidence counts for diagonal basis. Blue and green open triangles: filtering losses for signal and idler photons, respectively.

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4. Conclusion

In summary we successfully generated wavelength-multiplexed polarization-entangled photon pairs by using cascaded SFG/SPDC in a PPLN ridge waveguide device. We observed clear two-photon interference fringes and visibilities higher than 98% for all the wavelength channels under investigation (eight pairs). Cross-talk to adjacent channels was less than −20 dB, and this value is expected to be improved by using recent AWG devices with lower cross-talk characteristics. The detuning characteristics of the pump wavelengths revealed that the system exhibited no significant changes even with 25 nm of wavelength detuning, implying that a wavelength-multiplexed QKD system consisting of more than 50 independent pairs of wavelength-multiplexed channels is possible with this photon-pair source.