1. Introduction

Frequency multiplexing for photonic entanglement distribution is a promising method for increasing capacity in quantum communication. Particularly in optical fiber communication, technologies for wavelength division multiplexing (WDM) have the potential to expand over hundreds of channel modes without modifying the fiber structure [1]. Thus far, experiments on frequency multiplexing have been actively conducted [2–7]. Therein, entanglement distribution has been performed by conventional broadband entangled photon-pair generation based on spontaneous parametric down-conversion (SPDC) followed by application of WDM-compatible frequency filters developed for fiber-optic communication. Recently, such schemes have been successfully employed in various applications for quantum communication among multiple users using polarization [8–12] and time-bin [13–15] encodings of photons. However, the separation of broadband SPDC photon pairs over the channels inevitably wastes a large amount of photon energy for sufficient suppression of channel cross-talk, which causes photon pairs to have a low brightness. SPDC inside a cavity, called cavity-enhanced SPDC [16–18], can be used to overcome this problem. Because this process gathers photon energies into resonant peaks with a frequency spacing determined by the cavity, the produced photon pairs show a joint spectrum with a comb-like structure called a biphoton frequency comb [6,19–21]. Consequently, by designing the free spectral range (FSR) of the cavity used for SPDC to be the same as the channel spacing of the WDM standard, efficient and precise extraction of photon pairs from a biphoton frequency comb to each channel of the WDM system can be achieved [22].

For this purpose, we experimentally showed frequency-multiplexed polarization-entangled photon-pair distribution using a polarization-entangled biphoton frequency comb via a singly resonant periodically poled lithium niobate waveguide resonator (PPLN/WR) [23] inside a Sagnac-type interferometer [20]. The length of the waveguide resonator with mirror coatings to the end faces was designed to be an FSR of 12.5 GHz, which was compatible with the dense WDM (DWDM) standard. Using DWDM-based frequency filters with a channel spacing of 25 GHz, we achieved distribution of polarization-entangled photon pairs over 16 channels. The fidelities of the reconstructed quantum states to the maximally entangled state in the 16 channels ranged from 81 % to 96 %.

2. Experimental setup

The experimental setup is shown in Fig. 1. A continuous-wave light of 780.240 nm enters a Sagnac-type interferometer as the pump light for SPDC. Horizontal (H-) and vertical (V-) polarized components of the pump light are split into counter-clockwise (CCW) and clockwise (CW) Sagnac loops, respectively, at a polarizing beamsplitter (PBS). In the CW loop, the V-polarized pump light is directly coupled to a PPLN/WR. In contrast, in the CCW loop, the polarization of the pump light is inverted from H to V using a half-wave plate (HWP). Subsequently the V-polarized pump light is coupled to the PPLN/WR.

 

Fig. 1. (a) Experimental setup. PBS: polarizing beamsplitter; HWP: half-wave plate; QWP: quarter-wave plate; DM: dichroic mirror; WDM: wavelength-division multiplexing; PPLN/WR: periodically poled lithium niobate waveguide resonator; SNSPD: superconducting nanowire single-photon detector. (b) Photon pair generation rate at different wavelengths. Orange curve represents photon pair generation rate of SPDC, which is calculated based on phase-matching condition of PPLN. Blue curve represents photon pair generation rate of cavity-enhanced SPDC, which is calculated based on reflectance of PPLN/WR used in our experiments. Curve is averaged over 3 nm bandwidth frequency filter and appropriately rescaled. Inset shows 16 channels for signal and idler photons used in our experiments.

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The PPLN waveguide used in our experiments satisfies the type-0 quasi-phase matching condition for the V-polarized light. Consequently, V-polarized photon pairs are produced by the SPDC process with the V-polarized pump light for both directions. As expected, the waveguide length of 5.6 mm achieves the photon-pair generation over a 100 nm bandwidth, as shown in Fig. 1(b). To produce a biphoton frequency comb within the region, the cavity structure of the PPLN waveguide is achieved using dielectric multilayers on the end faces of the waveguide. A high-reflective coating of approximately 96 % is achieved for the signal photons at longer wavelengths of approximately 1581 nm. On contrast, the reflectances of the idler photons at shorter wavelengths of approximately 1540 nm and the pump light at 780.787 nm are 40 % and 0.4 %, respectively. Although the non negligible reflectance of the idler photons fluctuates the photon generation rate, the singly resonant configuration avoids the cluster effect that photon pair generation is limited within specific spectral ranges observed in doubly resonant configuration [24,25]. As a result, we achieve efficient photon-pair generation over 100 nm with the FSR of 12.5 GHz of the cavity. The simulation of the photon-pair generation rate with the cavity structure is shown in Fig. 1(b).

The polarization of the photon pairs produced by the CW direction is inverted from V to H by the HWP, following which they are extracted after passing through the PBS. The V-polarized photon pairs produced by the CCW direction are extracted after reflection at the PBS. These photons are coupled to a polarization-maintaining fiber (PMF). Following this, the signal (long-wavelength) and idler (short-wavelength) photons are separated into two PMFs using a fiber-based CL band splitter with a pass band of 1500–1564 nm and a reflection band of 1570–1610 nm. Subsequently, the demultiplexer (DeMux) distributes the signal and idler photons over 16 channels with a channel spacing of 25 GHz. The center frequencies of channel $j$ ($= 1,\ldots, 16$) for the signal and idler photons are $f_{s,j} = 189.781 - 0.025 j$ THz and $f_{i,j} = 194.450 + 0.025 j$ THz, respectively, which are designed to satisfy the energy conservation as $f_{s,j} + f_{i,j} = f_p$. In the expression, $f_p$ is the pump frequency corresponding to a wavelength of 780.240 nm. For example, the signal/idler wavelengths corresponding to $f_{s,1}/f_{i,1}$ and $f_{s,16}/f_{i,16}$ are 1579.884 nm/1541.548 nm and 1583.012 nm/1538.581 nm, respectively.

Finally, the generated photons are detected by superconducting nanowire single-photon detectors (SNSPDs) [26]. Ideally, each of the photon pairs distributed over the 16 channels is in an entangled state, expressed as $| {\phi _\theta } \rangle _{s,i}:=(| {HH} \rangle _{s,i} + e^{i\theta }| {VV} \rangle _{s,i})/\sqrt {2}$, where $| {H} \rangle _{s(i)}$ and $| {V} \rangle _{s(i)}$ represent the H- and V-polarized single photon states in the signal (idler) mode, respectively. To evaluate the quality of the experimentally obtained photon pairs, polarization analyzers are inserted, each of which is composed of a quarter-wave plate (QWP), an HWP, and a PBS, into the optical paths of the signal and idler photons before the DeMux.

3. Experimental results

The SPDC photons extracted from the Sagnac interferometer include not only the desired state described in the previous section but also unwanted components $| {HV} \rangle _{s,i}$ and $| {VH} \rangle _{s,i}$ because signal photons are emitted from both ends of the PPLN/WR. For example, the signal photons produced by the pump light in the CW direction are extracted as H- and V-polarized photons after the interferometer via the CW and CCW directions, resulting in $| {HH} \rangle _{s,i}$ and $| {VH} \rangle _{s,i}$, respectively. Similarly, $| {VV} \rangle _{s,i}$ and $| {HV} \rangle _{s,i}$ are produced by the pump light in the CCW direction. $| {HH} \rangle _{s,i}$ and $| {VV} \rangle _{s,i}$ have the same optical path lengths as the signal photons, and thus, they form $| {\phi _\theta } \rangle _{s,i}$. However, for the two unwanted components, the path lengths of the signal photons depend on the position of the PPLN/WR. Consequently, by shifting the PPLN/WR from the center of the interferometer, both unwanted components can be temporally separated from $| {\phi _\theta } \rangle _{s,i}$, and thus, removed in time-resolved coincidence measurements.

We measured the arrival times of the signal photons based on the detection timing of the idler photons. The experimental results are shown in Fig. 2. As expected, the histograms of the coincidence counts of $| {HH} \rangle _{s,i}$ and $| {VV} \rangle _{s,i}$ overlap. However, those of $| {HV} \rangle _{s,i}$ and $| {VH} \rangle _{s,i}$ are separated from the desired middle peaks because of the difference in the optical path lengths. Based on these results, we set the coincidence window to be 3 ns around the middle peak of the coincidence counts in the following experiments, as shown in Fig. 2.

 

Fig. 2. Coincidence count as function of arrival time.

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The temporal shape of the coincidence counts reflects the singly resonant configuration of the PPLN/WR. From the best fit of a function for delayed time $\tau$ expressed as [20]

We performed quantum state tomography of the two-photon states for the 16 pairs of the channels. Using the iterative maximum likelihood method [27,28], we reconstructed the quantum state $\rho$ for each pair of the channels. From the result, we calculated the entanglement of formation (EoF) [29], fidelity defined as $F(\rho ) := \max _\theta \langle {\phi _\theta } |\rho | {\phi _\theta } \rangle$, and purity defined as $P(\rho ):={{\rm tr}}(\rho ^{2})$. The estimated values for all channels are shown in Figs. 3(a) – (c). The averages (standard deviations) of the EoF, fidelity, and purity are 0.81 (0.07), 0.90 (0.04), and 0.90 (0.05), respectively. The observed values of the EoF and the fidelity show that high-quality entangled photon pairs are produced for all channels. In addition to the observed purity, the SPDC photons in all pairs of the channels are produced at almost the same excitation rate. Consequently the observed count rate fluctuates slightly more than the other properties, as shown in Fig. 3(d). However, the cause is not the photon-pair source based on the PPLN/WR but the channel dependency of the transmittance of the optical circuit, including the DeMux for photon distribution placed after the polarization analyzers. Equalization of the photon-pair distribution rate under such a biased scenario among the channels has been addressed by adaptive bandwidth management in Ref. [10], which can be applied to our system.

 

Fig. 3. Observed values of (a) EoF, (b) fidelity, and (c) purity of photon pair in each frequency channel. (d) Number of counts of two-photon state $\rho$ observed in 1 min in each channel.

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4. Conclusion

In conclusion, we successfully distributed polarization-entangled photon pairs over 16 different channels with a channel spacing of 25 GHz. The observed fidelities of the polarization entanglement ranged from 81 % to 96 % with an average of 90 %. In the experiments, we developed a polarization-entangled biphoton frequency comb that meets the DWDM standard with SPDC-based photon-pair generation inside a cavity only for the signal photon of each photon pair. The FSR of the cavity was 12.5 GHz, which suggests that the photon spectrum has two peaks in each channel. Although this spectrum can be regarded as a single mode because of the superposition of the two peaks, this approach will limit the possibility of applications including high-quality entanglement swapping of the photons in each channel. The use of a shorter length of the PPLN/WR, such as 2.8 mm, for a 25 GHz comb spacing or a DeMux with a 12.5 GHz channel spacing is significant for realizing future applications. Photon pairs based on SPDC using a singly resonant cavity configuration were produced over a range of 80 nm without the clustering effect [20], which corresponds to approximately 800 frequency modes (400 photon pairs) with a 12.5 GHz channel spacing. We believe that the developed photon-pair source will be useful for large-scale frequency-multiplexed entanglement distribution and other quantum network applications.