Entangled photon pairs are a very important resource for testing quantum mechanics foundations [1] and realizing various photonic quantum technologies [2]. All these applications require a high-brightness and reliable entanglement source. In recent decades, the spontaneous parametric down-conversion (SPDC) process is a successful technique to generate the entangled photon pairs.

Due to the high second-order nonlinear susceptibility ($ {\chi ^{(2)}} $) and flexible frequency-tunable processes, the quasiphase-matching (QPM) SPDC is extensively used in experiments [3]. Introducing the periodic ferroelectric domain inversion in the nonlinear crystals, such as periodically poled lithium niobate (PPLN) and potassium titanyl phosphate (PPKTP), is an easy way to get the QPM interactions in a nonlinear crystal. In particular, the engineered QPM structures can provide a set of reciprocals for multiple QPM interactions simultaneously in a single nonlinear crystal [4–10]. Besides, combining the PPLN with the mature waveguide fabrication technique, a fully integrated source can be achieved [11–13].

Based on the QPM technique, early sources of polarization entanglement are directly generated by a postselection method which is by using a beam splitter (BS) to separate the collinear orthogonally polarized photon pairs from a type-II SPDC process [14,15]. However, this method suffers a 50% loss. To avoid this loss, the method of introducing interference of two pairs of orthogonally polarized photons on a polarization beam splitter (PBS) which are generated by bidirectionally pumped periodically poled (PP) crystal [16–19], or by two SPDC sources [20,21] was developed. However, these sources are not compact and require phase control in the interferometer. While for a frequency-nondegenerate source, a compact method was demonstrated by cascading two SPDC sources in a single crystal [22,23]. However, due to the two SPDC processes that are separated in the nonlinear crystal, the coherent length of the pump light should be longer than the length of PP crystals, and thus, the length of a PP crystal is limited.

In this Letter, we demonstrate a dual-periodic-poled $ {\rm Ti}:{{\rm LiNbO}_3} $ waveguide to generate the nondegeneracy polarization-entangled photon pairs. We set the wavelength of down-conversion photons in the telecommunication window. By appropriate design, we can realize two concurrent and coherent nondegenerate type-II SPDC processes in a single waveguide, explicitly, $ {H_{{\lambda _p}}} \to {H_{{\lambda _s}}} + {V_{{\lambda _i}}} $, $ {H_{{\lambda _p}}} \to {H_{{\lambda _i}}} + {V_{{\lambda _s}}} $, where $ {\lambda _p} $, $ {\lambda _s} $, and $ {\lambda _i} $ denote the wavelengths of the pump, signal, and idler fields, respectively, $ H $ ($ V $) representing the horizontal (vertical) polarization. In the single-mode approximation, the two-photon term of the state generated from the two SPDC processes can be written as [8]

 

Fig. 1. Schematic of a dual-periodically-poled $ {\rm Ti}:{{\rm LiNbO}_3} $ waveguide. The black strip area is the waveguide. Gray and blank areas are inverted ($ - {\chi ^{(2)}} $) and background positive ($ + {\chi ^{(2)}} $) domains, respectively.

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The sample used in our experiment is fabricated in our laboratory based on the dual-periodic poled $ {\rm Ti}:{{\rm LiNbO}_3} $ waveguide, where the substrate is z-cut, and the thickness is 0.5 mm. The waveguide is fabricated by the metal titanium strip with the width $ w = 6.5\;\unicode{x00B5}{\rm m} $, the height $ \tau = 70\;{\rm nm} $, and the length $ L = 11\;{\rm mm} $. First, we make the diffusion for 7 h at 1050°C in an oxygen environment. Next, we carry out the room temperature poling process to induce the inverse ferroelectric domain in the waveguide for the dual-periodic QPM processes [26]. Finally, the sample is polished to insure the pump and parametric light coupled into and out of the waveguide, respectively. The loss of the PPLN waveguide is measured to be 0.3 dB/cm for parametric light. The waveguide is single mode for parametric light, while it is multimode for the pump light. In the experiment, by carefully coupling, we make the pump laser mainly inspire the single mode.

In the experiment, we first test the QPM processes of the sample by means of the sum frequency generation (SFG) process, where we utilize two wavelength-tunable lasers, one in the O-band window (Santec TSL-550) and the other in the CL-band window (Santec TSL-710). The two laser beams are combined into one beam by a dichroic mirror (DM) and coupled into the waveguide by an achromatic lens. The operating temperature is set to 100°C. For testing the QPM process of the first period, the light from an O-band CW laser with the horizontal polarization, is coupled into the waveguide to excite the TE mode. On the one hand, the light from a CL-band CW laser with vertical polarization and coupled into the waveguide to excite the TM mode. By first fixing the TE mode wavelength and then tuning the TM mode wavelength for maximal SFG light output power, we obtained the QPM curves as shown in Fig. 2 which are linearly fitted by solid lines. The QPM curves of the second period is obtained analogously by setting the O- and CL-band CW laser light to V and H polarization, which is shown in Fig. 2 (dashed line). The two crossing points correspond to the working SPDC processes, namely, $ {H_{704.1\,{\rm nm}}} \to {V_{1489.9\,{\rm nm}}} + {H_{1335\,{\rm nm}}} $ and $ {H_{704.1\,{\rm nm}}} \to {H_{1489.9\,{\rm nm}}} + {V_{1335\,{\rm nm}}} $. Hence, by the classical SFG process test, we have proved that the sample used in our experiment can support concurrent SPDC processes in a single dual-periodically-poled $ {\rm Ti}:{{\rm LiNbO}_3} $ waveguide. The entangled photon pairs can be obtained by pumping the waveguide at the wavelength of 704.1 nm with the horizontal polarization.

 

Fig. 2. Measurement results of sum frequency generation processes: solid lines correspond to the first period, and the dashed lines correspond to the second period. The intersection of the two phase-matching curves is the operation point for us to generate the polarization-entangled photons.

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The setup for measuring our polarization-entangled photon-pair source is sketched in Fig. 3. The pump laser at the wavelength of 704.1 nm is achieved by using a tunable external-cavity diode laser (Thorlabs HL7001MG), and the linewidth is about 0.02 nm. For achieving type-II SPDC processes in the waveguide, we prepare the pump light to horizontal polarization by a fiber polarization controller (FPC), and then the pump light is coupled into the waveguide by a lens. The nondegeneration polarization-entangled photon pairs are generated and coupled out from the waveguide by an achromatic lens. Due to the group velocity dispersion of the $ {\rm Ti}:{{\rm LiNbO}_3} $ waveguide, the temporal delay between the photons generated in the same process will be induced. For compensating the relative delay, a 5.5 mm-length x-cut and y-propagation lithium niobite birefringent crystal is put after the waveguide [27]. By using a DM, the nondegeneration photon-pairs at different wavelengths of 1335 and 1489.9 nm are reflected and transmitted into different paths, respectively. For testing the entanglement source, a half-wave plate (HWP) and a PBS are inserted into the two paths before the single photon detectors. In the transmission path, two 45° quarter-wave plates (QWPs) sandwiched by a HWP are used to tune the relative phase $ \Phi $ finely, which is caused by the dispersion effect of the frequency-nondegenerate photon pairs with polarization HV and VH, respectively. Then, photons are coupled into a single mode fiber and routed to the photon detector. The photons at the wavelength of 1489.9 nm are detected by IDQ220. The photons at the wavelength of 1335 nm are detected by IDQ201 which is triggered by the photon detector IDQ220, and the coincidence counts are recorded.

 

Fig. 3. Schematic of the experimental setup. The nondegeneration polarization-entangled photon pairs are separated by a dichroic mirror (DM). Emerging from the waveguide, the entangled photons pass through a half-wave plate (HWP) and a PBS; the photons are coupled by a fiber and routed to single photon detector IDQ220 or IDQ201 followed by a coincidence measurement apparatus. The Bragg gratings are filters to get rid of the unwanted photons.

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However, the photon pairs have slightly different spectral shapes in the sidelobes due to unideal fabrication. For getting the indistinguishable photon pairs, we inserted a narrow-band Bragg grating filter system in the transmission path. The full width at half maximum (FWHM) of this filter is about 2 nm, and the FWHM of the SPDC spectrum generated in the waveguide is about 2.3 nm. We note that the signal and idler photons are nearly optimally frequency-anticorrelated because we use the cw pump laser with and without the filter [28]. In the reflected path, a Bragg grating filter system with FWHM is about 6 nm and is used to get rid of the unnecessary photons. We fix one of the HWPs at the angles of 0, 22.5, 45, and 67.5 deg, respectively, and measure the two-photon coincidence counts as a function of another HWP rotation angle. We note that for each measurement below, we estimate the accidental coincidence counts by tuning the time delay away from the peak position at the detector IDQ201, which is about 15 Hz. The accidental coincidence counts result from background light and multiphoton contributions of SPDC, which are subtracted in the following data. As a result, we get the interference visibility above 94.5%, as shown in Fig. 4. According to the method of Clause, Horne, Shimony, and Holt (CHSH) [29], we set the HWPs at specific angle combinations to get coincidence counts for calculating the violation of the Bell inequality, and we obtain the $ S $ parameter to be $ S = 2.75 \pm 0.03 $, which confirming a strong violation of Bell inequality by 25 standard deviations. To fully characterize our quantum state, we take the quantum state tomography [30] to reconstruct the density matrix of the entangled photons, with the real and imaginary parts shown in Fig. 5. The fidelity of the quantum state is $ F(\psi ,\rho ) = \langle \psi |\rho |\psi \rangle = 0.945 \pm 0.003 $, and the concurrence is $ C = 0.909 \pm 0.02 $ [31]. These results demonstrate that we have the high-quality polarization-entangled photon-pair source. The nonideal fidelity results from the different spectral shapes of the two SPDC processes due to the nonideal fabrication of waveguide and poling. A much narrower band filter could be used to improve the fidelity.

 

Fig. 4. Correlation measurements for four different bases: H/V (black/red) and diagonal D/A (blue/green). The pump power is about 1.37 mW, measured after the waveguide.

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Fig. 5. (a) Real and (b) imaginary part of the experimental density matrix of the state generated by our source.

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In conclusion, we have experimentally demonstrated a novel and stable way to produce the polarization-entangled photon pairs based on a dual-periodically-poled $ {\rm Ti}:{{\rm LiNbO}_3} $ waveguide. The source employs two inherently concurrent type-II QPM SPDC processes in a single waveguide. The experimental results have shown that the source has a high-quality performance with a fidelity of $ 0.945 \pm 0.003 $. The production rate of polarization-entangled photon-pair source in the waveguide is about $ N = 2.8 \times {10^7}\;{\rm pairs}/({\rm s} \times {\rm mW}) $ estimated with the heralding efficiency, correspondingly, the brightness of our source is as high as $ B = 1.22{\rm } \times {10^7}\;{\rm pairs}/({\rm s } \times {\rm mW } \times {\rm nm}) $. The raw heralding efficiency can be calculated to be 0.2%. Considering the detector efficiencies of 15% and 25%, the corrected heralding efficiency is about 5.4%. One reason for the low heralding efficiency is the reflection loss at the end faces of the waveguide and the birefringent crystals which are all not antireflection coated. The losses can be effectively decreased with antireflection coating. Another main reason is the nonideal coupling into the fibers, which could be solved with an overall pigtailed vision. The source only requires a single one-direction pump light, and thus one single-mode fiber can couple the pump light into the waveguide. The compensating birefringent crystal can also be replaced by the polarization-maintaining fiber (PMF). Besides, the DM and filters can be replaced by the fiber demultiplexer and fiber filters as well. Consequently, the source could have a overall pigtailed vision and may be compatible with the quantum fiber networks [32]. Moreover, for realizing a fully integrated active quantum chip, it will be possible to integrate the on-chip waveguide devices [11,12,33,34] with our source. And this source will meet the need of completely integrated source [35].