1. Introduction

Entanglement is an essential resource for quantum information systems such as quantum key distribution (QKD) [1] or quantum computers [2]. To realize quantum information systems over optical fiber networks, it is very important to establish a way to generate entangled photons in the 1.5-µm band. There have been several reports on such 1.5-µm band entangled photon sources, including sources based on spontaneous parametric downconversion (SPDC) in periodically poled lithium niobate (PPLN) waveguides [3, 4, 5], spontaneous four-wave mixing (SFWM) in dispersion shifted fibers (DSF) [6, 7], and SPDC in bulk crystals [8]. Of these, the DSF-based entangled photon source is promising because of its good connectivity to transmission fibers. In addition, the photon timing jitter caused by the “walk off” between a pump pulse and a photon pair is usually negligible in an SFWM-based photon-pair source, because the four photons involved in the nonlinear process have similar frequencies and so the group velocity mismatch is negligible. As a result, it was shown that the photons from two independent DSF-based photon-pair sources exhibited quantum interference [9]. This characteristic makes the entanglement source a promising candidate for a quantum relay, which is a QKD based on entanglement swapping [10, 11].

However, there is a drawback with DSF-based entanglement sources, namely noise photons generated by spontaneous Raman scattering (SpRS) [6, 7, 12]. Although SpRS photons can be significantly reduced by cooling the fiber [13], the use of cooling equipment complicates the entire system and is thus undesirable.

Recently, SFWM in a nano-scale silicon waveguide has been attracting attention as a way of generating correlated photon pairs [14, 15]. Since the Raman spectrum of single crystal silicon is 15.6 THz away from the pump frequency with a width of about 100 GHz, the SpRS photons in silicon are significantly suppressed by setting the signal/idler frequencies away from the Raman peak [16]. We have already reported the first entanglement generation experiment using a silicon waveguide, which was based on time-bin qubits [17]. Although time-bin entanglement is suitable for fiber transmission [18], entangled photons based on polarization qubits are important for many quantum information processing tasks such as quantum teleportation [19], entanglement swapping [20], and entanglement purification [21, 22]. In this paper, we report the generation of polarization entanglement using a silicon wire waveguide. By placing the silicon waveguide in a fiber loop that is similar to the one used in citetakesue1,li2,ful,fan, we have successfully generated polarization entangled photon pairs.

2. Experimental setup

 

Fig. 1. Experimental setup. PBS: polarization beam splitter, PC: polarization controller.

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Figure 1 shows the experimental setup. A 90-ps pump pulse with a wavelength of 1551.1 nm and with a 100-MHz repetition rate was passed through a polarizer, a polarization controller (PC) and a circulator, and input into a fiber loop. The loop consisted of a polarization beam splitter (PBS), two PCs and a silicon wire waveguide. The polarizer angle and the PC in front of the circulator were adjusted so that the polarization state immediately before the PBS exhibited 45-degree linear polarization. The pump pulse was split into horizontal (H) and vertical (V) polarization components with the PBS, which circulated in the loop in the counter-clockwise (CCW) and clockwise (CW) directions, respectively. At the silicon wire waveguide, the CCW (CW) pump pulse probabilistically created a photon pair state |CCW〉_s|CCW〉_i (|CW〉_s|CW〉_i) through SFWM, where |X〉_y denotes a state in which there is a photon in the X direction (or a polarization state in the later case) and in mode y (=s, i; s: signal, i: idler). The PCs in the loop were adjusted so that the polarization states of both the CCW andCW pumps were aligned with the same silicon waveguide axis. With this configuration, the state |CCW〉_y (|CW〉_y) generated in the waveguide was converted to |V〉_y(|H〉_y), and output from the loop through the PBS input port. As a result, we obtained a maximally entangled state (|H〉_s|H〉_i +|V〉_s|V〉_i)/√2 at the output port of the circulator by employing a relatively low pump power thus minimizing the probability of the simultaneous generation of both |CCW〉_s|CCW〉_i and |CW〉_s|CW〉_i states. The photons from the circulator were passed through a fiber Bragg grating to suppress the pump, and launched into an arrayed waveguide grating to separate signal and idler photons. The signal and idler wavelengths were 1547.9 and 1554.3 nm, respectively, and both had a 0.2-nm bandwidth. The bandwidth was measured using an optical spectrum analyzer with a wavelength resolution of 0.007 nm. The signal and idler photons were then filtered by bandpass filters to further suppress the pump, and input into polarization compensators to make the Jones matrices of the signal and idler paths the same. The full widths at half maximum of the transmittance spectra of the bandpass filters were both 0.8 nm, and the losses at the peak transmittance points were 1.0 dB (signal) and 1.2 dB (idler). Then, each photon was transmitted through a rotatable polarizer, and detected by an InGaAs/InP avalanche photodiode (APD) operated in a gate Geiger mode at a frequency of 10 MHz. The temporal width of the gate was set at 1.4 ns. The 10-MHz gate signal to the APDs was synchronized with the 100-MHz pump pulses. We used a 100-MHz pump frequency so that we could easily capture a pulse in a gate with a small change in the gate delay time. The quantum efficiencies of the detectors were both 10%, and the dark count rates per gate were 1.4×10^-5 (signal) and 3.2×10^-5 (idler). The signal and idler channel losses were 15.7 and 12.6 dB, respectively. The detection signals from the idler and signal channels were input into a time interval analyzer as start and stop pulses, respectively, to record coincidence counts.

The silicon wire waveguide was fabricated on an silicon-on-insulator (SOI) wafer with a silicon top layer on a 3 µm SiO₂ layer [26]. The waveguide was 460 nm wide, 220 nm thick and 1.09 cm long, and required no temperature control. The waveguide loss was 3.1 dB, and the effective area of the waveguide was calculated to be 0.04 µm² [27]. Thanks to this small effective area, the estimated nonlinearity coefficient exceeded 10⁵ 1/W/km [17]. The waveguide coupled peak pump power to each facet was around 60 mW, and we used it to generate polarization entangled photon pairs with an average photon-pair number per pulse of about 0.05.

3. Result

We fixed the polarizer angle of the signal θ_s, and measured the single and coincidence count rate while rotating the idler polarizer angle θ_i. Figures 2 and 3 show the coincidence rate per start pulse and the idler count rate as a function of θ_i, respectively. Here, the squares and circles denote the rates when θ_s was set at 0 and 45 degrees, respectively. We observed clear modulation in the coincidence count rates for two non-orthogonal measurements performed for the signal photons, while the idler count rate was almost independent of θ_i. The slight change in the idler count rate observed in Fig. 2 was possibly caused by the polarization dependent loss of the polarizer for the idler channel. The coincidence rate at the peak of the fringe was 1.8 cps when θ_s=0. The coincidence at each idler polarizer angle was measured for a period in which 100,000 start pulses were recorded. Since the average idler count rate was ~1,800 as shown in Fig. 3, the measurement time for each point in Fig. 2 was approximately 55 s. 102 coincidence counts were obtained at the peak of the fringe. The visibilities of the fitted curves were 95.9±9.0% for θ_s=0 and 82.9±7.1% for θ_s=45 degrees. These results confirmed the successful generation of entangled photon pairs with high visibilities using a silicon wire waveguide. The visibility degradation in the fringe for θ_s=45 degrees was probably due to imperfect polarization adjustment in the signal and idler channels.

 

Fig. 2. Two-photon interference fringes. Squares: θ_s=0 degrees, circles: θ_s=45 degrees.

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4. Discussion

The full width at half maximum of the photon pair temporal width was 18 ps, which is about one fifth of the pump pulse width. In this parameter regime, the number distribution of the photon pairs is well approximated with a Poissonian [28]. When x photons are incident on a threshold single photon detector (i.e. a photon detector without photon number resolving capability), the detection probability is given by 1-(1-α)^x, where α denotes the collection efficiency including the quantum efficiency of the detector. When α≪1, the detection probability is approximated as xα. In our setup, α was 2.7×10^-3 for the signal and 5.5×10^-3 for the idler, and so we can use this approximation in the following equations.

If we suppose that no noise photons are generated in our entangled photon pair source, the coincidence probability caused by correlated photons at the peak of the two-photon interference fringe is expressed as

Here, µ, α_s and α_i are the average photon-pair number per pulse, signal collection efficiency, and idler collection efficiency, respectively. On the other hand, the probability of accidental coincidences caused by uncorrelated photons and detector dark counts is approximated by

 

Fig. 3. Idler count rates as a function of idler polarizer angle. Squares: θ_s=0 degrees, circles: θ_s=45 degrees.

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where d_s and d_i denote the detector dark count per gate for the signal and idler channels, respectively. The factor 1/2 is present in the above two equations because we used a polarizer followed by one detector for each channel and so we discarded half of the photons. Since the maximum I_max and miminum points I_min in a two-photon interference fringe are given by R_c+R_acc and R_acc, respectively, the visibility of the two-photon interference fringe is given by

Using the parameters given in the previous sections, the theoretical visibility for µ=0.05 is calculated to be 93.1%, which is close to the experimental result for θ_s=0 degrees. This implies that we have not observed noise photons in our two-photon interference experiments, and thus proves that our entanglement source has low-noise characteristics.

We note that a team from Northwestern and Cornell Universities has reported a polarization entanglement generation experiment using a similar loop configuration with a silicon chip during the preparation of this paper [29]. The important difference is that they only showed a fringe for one measurement basis, while we obtained fringes for two nonorthogonal measurement bases. In theory, a coincidence measurement on a classically correlated state whose density matrix in the H-V basis is given by

shows a fringe if the measurement is undertaken only with the H-V basis. Clearly, the fringe will disappear in a measurement, for example, with a diagonal basis. In contrast, an example entangled state is expressed as

According to this equation, an entangled state should show correlation in measurements with nonorthogonal bases. Therefore, our experimental result with two nonorthogonal bases gives better confirmation of entanglement generation. Although we believe that the present result clearly demonstrated the existence of entanglement, a more detailed characterization of our entanglement source is important future work. Experiments such as Bell’s inequality measurement [30] and quantum state tomography measurement [31] are suitable for this purpose.

One of the problems with the current experiment is the relatively large channel losses that made the coincidence rate very low. Although the channel losses are an accumulation of losses caused by many components, a large portion of the losses are from the coupling between the output of the silicon wire waveguide and the fiber. With the current setup, we used a fiber coupling system designed for larger waveguides such as a PPLN waveguide, which resulted in a relatively large coupling loss of approximately 4 dB. With an improved fiber coupling system, we can expect a coupling loss of <1 dB. It is also important to reduce the loss of other components such as the circulator, the fiber Bragg grating, and the arrayed waveguide grating so that we can make the entanglement source more practical.

A quantum correlation measurement reported in [17] suggests that fewer noise photons were generated by SpRS in the silicon wire waveguide than in a DSF at room temperature. However, we need a more thorough investigation to determine whether or not the SpRS photons are completely suppressed. For example, a temporal correlation measurement using detectors with better sensitivity, such as those based on superconducting devices [32, 33], can provide a good confirmation experiment.

The photon-pair generation efficiency obtained using the 3.1-dB loss waveguide is already as good as that of a 500-m DSF [17]. With the recent technological advancement, the loss of a silicon wire waveguide can be as small as <1.5 dB, and a length of up to ~6 cm is already available. According to the theory in [14], if we use a 4-cm long, phase-matched silicon wire waveguide with a 1.5-dB loss, the generation efficiency can be increased by approximately 5 times. Thus, we can expect further improvement of brightness in the near future.

5. Conclusion

We have reported polarization entangled photon pair generation using a silicon wire waveguide. We employed a fiber loop that contained a silicon waveguide to realize the stable generation of a maximally polarization-entangled state in the 1.5-µm band. We obtained a high-purity entangled state that showed >83%-visibility two-photon interference without temperature control. This result suggests that we may be able to construct a simple and robust entanglement source that consists of passive devices (other than the pump laser) without temperature control.