1. Introduction

Entangled photon sources are indispensable for nearly all types of research and applications in the quantum information science and technology (QIST) field [1,2]. The preparation of high-quality entangled photon sources has been a long-term aim in QIST. One commonly used method to generate quantum light sources is based on use of nonlinear processes such as spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM) [3,4]. Since the first observation of SPDC by Burnham in 1970 [3], SPDC has been used widely to generate various entangled photon source types. Because of the conservation of energy, linear momentum and angular momentum in SPDC, the generated photons can be entangled in various degrees of freedoms, including polarization [5–11], time-energy [12–14], time-bin [14–17], angular momentum [18–20] and position-momentum types [21–23].

Initially, researchers focused on the generation of entangled photon sources with a single degree of freedom. As one example, many experimental configurations can be used to generate polarization entanglement [5–11]. The most commonly used methods include the use of a single type-II phase matched nonlinear crystal [5], high-brightness beam-like designs for multi-photon experiments [9] and use of a nonlinear medium in a Sagnac loop [6,8,11,14,15]. These commonly used methods have distinguishing properties including simplicity, robustness, and high entanglement quality. Specific configurations are usually most suitable for single types of entanglement generation and practical demonstration of a preferred source for multiple quantum optical experiments such as two-photon Hong-Ou-Mandel interference, time-energy entanglement and multiplexed polarization entanglement has not been reported to date.

In this work, by tailoring the spectrum of an orthogonally-polarized photon pair generated from a thin type-II periodically poled quasi-phase matching crystal via a 100 GHz dense-wave-division-multiplexing (DWDM) device, we perform multiple quantum optical experiments including Hong-Ou-Mandel (HOM) interferometry, time-energy entanglement generation and characterization and multiplexed polarization entanglement generation and characterization. The near-unity visibilities in all three types of interference experiment demonstrate the high qualities of the three kinds of photon sources. The scheme presented here is very simple, robust, and fully compatible with telecommunications band technology and off-the-shelf commercial devices. The proposed setup will provide multi-functional photon sources that are highly promising for various areas of research and applications in QIST.

2. Results

2.1 Principles and experimental setups

We will first present the principle of the experiments in this work (Fig. 1). The emission spectrum of a thin periodically poled KTP crystal (PPKTP) is a sinc² function, and for the 2-mm-long PPKTP crystal used in our experiment, the full width at half maximum of the emission spectrum is 1230 GHz. The 32-channel DWDM device has channel frequency separation of 100 GHz (where the transmission width of each channel is 66 GHz, and 34 GHz is used for channel isolation; for full details of the ITU channel definition, please see the Appendix 4.1). By pumping the crystal with a wavelength that is half that of a specific channel (in our experiments, it is channel C34, its wavelength is 1550.12 nm) and tuning the crystal temperature to ensure degenerated emission of signal and the idler photons, the output channels can then be divided into two types by injecting the photons to the common port of the DWDM device. The central channel C34 has orthogonal signal and idler photons that are degenerated and correlated (see the red block), these correlated photons can be further separated to perform HOM interference and time-energy entanglement measurements; for all other channels (S1–S6, I1–I6), although the channel contains orthogonal photons, they come from the uncorrelated frequency part of the source and there is no correlation between these orthogonal photons. A photon that is correlated with a specific channel lies on the other side of the central channel and has the same frequency shift from the central channel; these correlated channel pairs can be used to generate multiplexed polarization entanglement.

 

Fig. 1. Operating principle and experimental setups for versatile photon sources. (a) Simulated spectrum of the emitted photon pair and the transmission spectrum of the 100 GHz DWDM; (b) experimental setup before the photons are coupled out from the DWDM; (c) experimental setup for HOM interference; (d) experimental setup for two-photon Franson interference; (e) experimental setups for polarization entanglement generation and characterization. PPKTP: periodically poled potassium titanyl phosphate; Q/HWP: quarter/half wave plate; PBS: polarizing beam splitter; FC: fiber coupler; PC: polarization controller; FBS: fiber beam splitter; UMI: unbalanced Michelson interferometer; SNSPD: superconducting nanowire single photon detector.

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The experimental setups are shown in Fig. 1(b)–1(e). The pump laser wavelength is 775.06 nm (TA Prodesign, Toptica; linewidth <1 MHz) and the pump beam polarization is set to horizontal polarization by using a group of half-wave and quarter-wave plates to achieve type-II SPDC in PPKTP. The pump beam is focused into a 2-mm-long PPKTP crystal (Raicol Crystals, 46.2 µm poling period) with a 100 mm focal length, and then a 100-mm-focal length lens is used to align the beam for collection in a single-mode fiber (SMF) with a fiber collimator. Before collection into the SMF, the photon is first transmitted through a KTP crystal (1 mm long, with its optical axes aligned orthogonally with respect to the PPKTP crystal) to compensate for the time walk-off between the signal and idler photons. The pump beam is removed using a long pass filter (FELH1400, Thorlabs). The photons collected in the SMF are injected into the common port of a 32-channel DWDM device. The output photons from the different channels are used to perform three types of experiments. We will introduce these experiments one by one in the following sections.

2.2 Characterization of HOM interference

We first use central channel C34 for HOM interference experiments. The photons from the central channel are emitted into free space again and then pass through a group of QWPs and HWPs for polarization control. The signal and idler photons with appropriate polarizations are separated using a polarizing beam splitter (PBS); the polarizations of the photons from the two output ports of the PBS are controlled separately with two groups of QWPs and HWPs and are then coupled into the two input ports of a fiber beam splitter (FBS). One of the FBS input ports is mounted on a one-dimensional translation stage to vary the relative delay between the interference photons. The FBS output ports are connected to two superconducting nanowire single-photon detectors (SNSPDs, 60% detection efficiency) for photon detection and coincidence measurement (Timeharp 260 Pico; 0.8 ns coincidence window). The experimental results are shown in Fig. 2(a). We measured the coincidence counts in a 5 s period as a function of the relative time delay between the two arms and obtained the interference visibility (V= (C_Max−C_Min)/C_Max) of 99.50 ± 0.12%, where C_Max and C_Min represent the maximum and minimum coincidence counts, respectively.

 

Fig. 2. Experimental results for the different types of photon source. (a) HOM interference fringes in 5 s as a function of the relative delay between the two photons; (b) two-photon Franson interference fringes for time-energy entangled source in 10 s for two phase settings; (c) polarization interference fringes in 10 s for the 0° and 45° bases; (d) interference visibilities on a 45° basis for other correlated channel pairs.

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The FWHM is 9.46 ps, which is consistent with the transmission bandwidth of the DWDM (66 GHz) [24]. In the experiments, the pump laser power at 775.08 nm is 256 mW. The single count rates for the two detectors are 2.1 × 10⁴ cps and 1.7 × 10⁴ cps. After interference with zero delay in the FBS, the photons are in the photon number and path entangled state $1/\sqrt 2 (|{2,0} \rangle + |{0,2} \rangle )$, which is promising for use in quantum enhanced metrology [25–27].

2.3 Characterization of time-energy entangled source

Next, we characterize the time-energy entanglement for central channel C34. The output ports of the PBS are connected to two unbalanced Michelson interferometers (UMIs) for two-photon Franson interference [28]. When the photons pass through both the long path and the short path of the two UMIs, they are indistinguishable, and can be expressed as the state of $|\Phi \rangle = 1/\sqrt 2 (|{LL} \rangle + |{SS} \rangle )$, where S and L stand for the long path and the short path, respectively. We obtain the interference visibility using V = (C_Max−C_Min)/(C_Max+C_Min). We maintain the phase of one UMI at constant values of 0 and π/4, and vary the phase of the other UMI by tuning the temperatures of the UMIs; the two UMIs have a time difference of 1.6 ns between their two arms [15]. The interference fringes are shown in Fig. 2(b), and the interference visibilities for the two phases are (99.17 ± 0.35)% and (99.59 ± 0.24)%, respectively, without subtraction of the accidental-coincidence counts. These near-unity visibilities indicate that the two photons have a high entanglement quality. In measuring the Franson interference of the time-energy entangled photon pair, the single counts of the two detectors were 7.3 × 10³ cps and 6.7 × 10³ cps.

2.4 Characterization of multiplexed polarization entangled source

Finally, we characterize the multiplexed polarization entangled source. Each of the correlated channels are connected to a fiber polarization controller and is then output to free space for projection measurements. The projection measurement setup contains QWPs, HWPs and a PBS. In one of the paths, a group of wave plates that consists of two QWPs and one HWP functions as an arbitrary phase retarder for tuning of the relative phase between the superposition states. The polarization state after the DWDM for the two correlated channel pairs is $|\Psi \rangle = 1/\sqrt 2 (|{H({\lambda_{s}})V({\lambda_{i}})} \rangle + {e^{i\theta }}|{V({\lambda_{s}})H({\lambda_{i}})} \rangle )$ [29], where H and V represent the horizontal and vertical polarizations, respectively; λ_s and λ_i represent the wavelengths of the signal and the idler, respectively; and θ is the relative phase between the two superposition states. To achieve polarization entanglement, the compensate KTP is used to remove the time walk off between signal and idler photons because of different group velocities [30]. Various methods, including polarization interference, the Bell inequality and quantum state tomography, are used in the experiments to characterize the quality of the entanglement source. A channel pair composed of channels C33 and C35 is used as an example. The polarization interference fringes are shown in Fig. 2(c) and the interference visibilities for the two angle sets yield values of (99.20 ± 0.11)% and (98.80 ± 0.14)%, respectively. In measuring the polarization interference of the polarization entangled photon pair, the single counts of the two detectors were 3 × 10⁴ cps and 1.6 × 10⁴ cps, respectively. To check the entanglement quality for different entangled channel pairs, we measured the interference visibility on a 45° basis angle, and the results are as shown in Fig. 2(d). All the correlated channel pairs show very high visibilities exceeding 97%. The single count and coincidence count rates for different channel pairs are added in appendix table 1. All these visibilities are high enough to violate the Bell inequality [31]. We then check the Bell inequality for the channel pair of C33 and C35 and the measured S parameter is 2.764 ± 0.0139, which violates the inequality with 55 standard deviations.

To determine the content of a quantum state fully, quantum state tomography should be used to reconstruct the density matrix of a quantum state [32]. The real and imaginary parts of the reconstructed density matrix are shown in Fig. 3(a) and 3(b), respectively. The fidelity of the reconstructed density when compared with the maximum Bell state is 0.9739 ± 0.0018, where the slight discrepancy from unity comes from the inaccurate rotation angles and imprecise retardation performance of the HWPs and QWPs.

 

Fig. 3. Reconstructed density matrix for polarization entangled photon pair for S1 and I1. (a) Real parts of the density matrix; (b) imaginary parts of the density matrix.

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3. Conclusions and discussions

In summary, we present a distinctive method to perform three types of quantum optical experiment based on a simple and robust configuration. The near-unity visibilities achieved in HOM interference, Franson interference and polarization interference experiments show that the photon sources have high entanglement quality. The photonic state after HOM interference can be used for high-precision quantum metrology [25–27,33], the nondegenerate polarization entangled state with large frequency separation can be used for ultra-sensitive quantum measurement by using the beat note in HOM interference [26]. For time-energy entanglement state, it can be used for quantum key distribution [17], besides this application, if other correlated channels are used, it can be used to create multi-photon time-energy entangled state [34] and generate bi-photon frequency comb for high dimensional entangled state generation in the time-energy domain [35]. The multiplexed polarization entangled state can be used for high-capacity quantum communications with the DWDM technique [36], though the methods for polarization entanglement generation is rather different. In the present work we are focus on entangled photon sources generation and characterization, all the possible applications of the present sources will be investigated on demand in our future researches. We should clarify that the present source has a relative low photon pair generation efficiency compared to other source using waveguide PPLN [37], the reason is that a short type-II phase matching bulk crystal is used here, but the total photon flux can be increased to the same level as in Ref. [37] by using higher pump power. Furthermore, by selecting suitable crystal lengths and bandwidths of the DWDM filters, the brightness and bandwidths of the photon pairs can also be engineered. These photonic sources would be suitable for widespread applications in multi-task QIST areas such as quantum metrology, quantum communication, and fundamental studies of quantum physics.

4. Appendix

4.1. Definitions of the wavelengths of the standard ITU grids and photon count rates

The corresponding wavelengths for the correlated signal and idler photons are defined in Table 1. The pump wavelength was 775.06 nm and the central wavelength for both the signal and the idler was located at the center of channel C34 (1550.12 nm). The table also gives the single count rates and coincidence counts rates for different channel pairs. Because of non-uniform in the transmission losses for different channels, the single count rates and coincidence count rates are non-uniform among different channel pairs.

Table 1. Definition of the wavelengths of the standard ITU grid for the signal and idler photons.

View Table

4.2 How the UMI phase is tuned in a time-bin source

The thermal coefficient of the fiber at 1550 nm is $\frac{{dn}}{{dT}} = 0.811 \times {10^{ - 5}}/{}^ \circ \textrm{C}$, and the fiber length difference of the UMI is 163.48 mm ($L{}_{d} = c\Delta t/2n$) for a 1.6 ns delay. The temperature for one tuning period $\Delta T = \lambda /(2{L_{d}}\frac{{dn}}{{dT}})$ is 0.585 K. In the experiments, the temperature tuning periods and the phases of the UMIs are measured and calibrated using a stable narrow-bandwidth laser source. The phases of the UMIs can remain unchanged for hours because they are seriously thermally and acoustically isolated from the environment and strictly temperature controlled using a homemade servo device.

Funding

Anhui Initiative in Quantum Information Technologies (AHY020200); China Postdoctoral Science Foundation (2017M622003, 2018M642517); National Natural Science Foundation of China (11934013, 61435011, 61525504, 61605194).

Acknowledgment

We thank David MacDonald, MSc, from Liwen Bianji, Edanz Editing China (www.liwenbianji.cn/ac), for editing the English text of a draft of this manuscript.

Disclosures

The authors declare no conflicts of interest.

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