1. INTRODUCTION

Integrated quantum photonic circuits [1] are an important platform for the implementation of quantum technologies due to their robustness to environmental disturbances, small size, and possible scalability to integrate many thousands of various quantum photonic devices [2], such as photon-pair sources [3–5], reconfigurable quantum networks [6], and single-photon detectors [7] on a single chip. Among these devices, entangled photon-pair sources using the spontaneous parametric down conversion (SPDC) process are of interest since they have been employed in many groundbreaking experiments such as initial demonstrations of quantum teleportation [8], the test of Bell’s inequality [9], and one-way optical quantum computing [10]. To achieve a high-performance on-chip SPDC photon-pair source, it is necessary to fabricate phase-matched low-loss waveguides with high-${\chi }^{(2)}$ materials. Conventional configurations typically require optimized dry-etching fabrication processes to minimize the propagation loss, which can be time-consuming, especially for novel ${\chi }^{(2)}$ materials. For instance, extensive efforts have been dedicated to optimizing the fabrication of low-loss photonic circuits on thin-film III–V-on-insulator [11–13] and lithium-niobate-on-insulator (LNOI) [14–19], making them ideal quantum photonic platforms. However, emerging new materials with high ${\chi }^{(2)}$ coefficients, such as ${\text{BaTiO}}_3$ [20] and ${\text{NbOCl}}_2$ [21], still require further efforts to optimize dry-etching processes to realize high-performance photon-pair sources. Some rib-loaded waveguide structures have been used [22–25] before the LN dry-etching process became mature, but a new configuration that does not rely on the dry-etching process completely and is compatible with various emerging ${\chi }^{(2)}$ materials would be highly desirable. Such a configuration could significantly reduce the time and resources required to develop high-performance quantum photonic devices using emerging high-${\chi }^{(2)}$ materials, ultimately accelerating the advancement of quantum photonic technologies.

Bound states in the continuum (BICs) systems can have low radiation loss of the confined states by making use of their destructive interference with the continuous modes. Recently, it was proposed and demonstrated that photonic BICs can exist in a low-refractive-index waveguide on a high-refractive-index substrate [26–28]. The destructive interference among various loss channels suppresses energy dissipation in the BIC-based waveguide, resulting in theoretically zero propagation loss. The BIC mechanism introduces a novel configuration to obtain ultralow-loss waveguides with the advantage of not requiring the dry-etching of the high-refractive-index materials. Based on BICs, various integrated photonic devices including low-loss waveguides, high-$Q$ microcavities [27,29], electro-optic modulators [27], and photodetectors [30] were realized. To date, however, all these BIC-based photonic devices are limited to the classical domains. Although BIC-based metasurfaces have been used for SPDC [31,32], integrated BIC photon-pair sources remain to be demonstrated. Low-loss propagation in BIC channels may classically be explained by the destructive interference [27] of scattered light radiating into unbound states, but low-loss propagation in the quantum regime, where a single photon exibits destructive interference with other photons, has yet to be demonstrated.

Here, we experimentally demonstrated integrated photon-pair sources using an etchless BIC waveguide on high-${\chi }^{(2)}$ materials. Specifically, we carefully defined the patterns of a low-refractive-index electron-beam resist waveguide (ZEP520A, $n_{@1560\mathrm{nm}}=1.543$, $n_{@780\mathrm{nm}}=1.549$ [33]) on top of the high-refractive-index ${\chi }^{(2)}$ material (lithium niobate, LN), so that light is confined by the BIC mechanism and satisfies a phase-matching condition for SPDC processes simultaneously. A continuous pump light at near-infrared wavelength 780 nm was used to generate entangled photon pairs at telecommunication wavelength 1560 nm. The on-chip generation rates reached megahertz level with an input power of 0.1 mW. We also measured a coincidence-to-accidental ratio (CAR) about 5773, and a heralded single-photon autocorrelation $g_{\mathrm{H}}^{(2)}(0)=0.174$. In the time-energy entanglement, a visibility of 94% was measured. Finally, we used three methods to get the measured pair generation rate, discussed the influence of imperfect measurement setup, and compared it with the theoretical generation rate. Our work demonstrating BIC-based photon-pair sources paves the way for the realization of etchless quantum photonic platforms using various emerging high-${\chi }^{(2)}$ materials.

2. MATERIALS AND METHODS

A. Device Design and Theory

The devices were fabricated on an LNOI substrate shown schematically in Fig. 1(a), with 150-nm-thick $z$-cut LN layer (purple) on 2-μm-thick silicon oxide (gray). We patterned a 600-nm-thick polymer waveguide (pink) with 5 mm effective length on the substrate. The fiber-to-chip coupling at two wavelengths is realized by two pairs of grating couplers. The directional coupler structure between the waveguide and grating coupler is designed to demultiplex 780 nm light and 1560 nm light [34]. Figure 1(b) shows the directional coupler that converts ${\mathrm{TM}}_0$ mode to ${\mathrm{TM}}_2$ mode at 780 nm and separates pump light and generated light. The fabrication process of the waveguide has been demonstrated in previous works [27,34]. We have improved the fiber-to-chip efficiency in this work.

 

Fig. 1. (a) Cross-sectional illustration of the waveguide structure which consists of a polymer waveguide on top of an LNOI substrate. (b) Schematic of the directional coupler with $w_1=3.4\mathrm{\mu m}$, $w_2=0.92\mathrm{\mu m}$, $\mathrm{gap}=0.35\mathrm{\mu m}$, and $L=162\mathrm{\mu m}$. (c) Simulated effective refractive indices of the ${\mathrm{TE}}_0,{\mathrm{TE}}_1,{\mathrm{TM}}_0,{\mathrm{TM}}_1$, and ${\mathrm{TM}}_2$ modes at 780 nm and the ${\mathrm{TE}}_0$ mode at 1560 nm as a function of the waveguide width $w$. The four insets show the corresponding electric field ($|\mathbf{E}|$) profiles. (d) Simulated propagation loss of the ${\mathrm{TE}}_0$ mode and ${\mathrm{TM}}_2$ mode as a function of the waveguide width $w$ at the respective wavelengths with specific thickness. The BIC point for the ${\mathrm{TM}}_2$ mode is indicated. (e), (f) Electric field ($|\mathbf{E}|$) profiles of the ${\mathrm{TE}}_0$ mode at SHG pump wavelength (e) and the ${\mathrm{TM}}_2$ mode at second-harmonic wavelength (f). (g) Normalized spectrum of second-harmonic generation from a fabricated device.

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The waveguide structure supports multiple modes with different polarizations. Figure 1(c) shows the simulated effective refractive indices of the fundamental transverse-electric (${\mathrm{TE}}_0$) mode at the telecommunication wavelength and several modes (${\mathrm{TE}}_0,{\mathrm{TE}}_1,{\mathrm{TM}}_0,{\mathrm{TM}}_1,{\mathrm{TM}}_2$) for the 780 nm wavelength with a varying waveguide width $w$. According to this refractive index curve, we chose the ${\mathrm{TE}}_0$ mode for the telecommunication wavelength and ${\mathrm{TM}}_2$ mode for the 780 nm wavelength to be phase matched without the need for periodic poling. The phase-matching point is where the effective refractive indices for the two modes are equal [35–37]. The electric field ($|\mathbf{E}|$) profiles of these two modes are depicted in Figs. 1(e) and 1(f), respectively. Figure 1(d) shows the simulated propagational loss of the two modes with a varying waveguide width $w$. From the propagational loss curves, we can see that the ${\mathrm{TE}}_0$ mode always has negligible propagation loss and the ${\mathrm{TM}}_2$ mode reaches zero propagation loss at the BIC point.

Normally, since the TE modes have a higher effective refractive index than the TM modes, the ${\mathrm{TM}}_2$ bound mode lies in the continuum of the TE modes. Light in the ${\mathrm{TM}}_2$ mode can interact with the TE continuous modes, causing energy dissipation to the substrate and introducing nonnegligible propagation loss. The energy is dissipated to the TE continuous modes at the two edges of the waveguide through multiple channels. When destructive interference happens among the multiple modes, the loss might be canceled. The decay length $L$ of the ${\mathrm{TM}}_2$ bound mode propagating in the waveguide can be expressed as $L\propto w^2/{\sin }^2(k_{y}w/2)$ [26,27], where $k_y$ is the $y$ component of the wave vector of the TE continuous mode which matches that of the ${\mathrm{TM}}_2$ bound mode. When $k_{y}w$ is a multiple of $2\pi ,L$ approaches infinity, and the ${\mathrm{TM}}_2$ bound mode becomes a BIC correspondingly. With careful design, the modal phase-matching condition and theoretically zero loss are realized simultaneously.

For waveguides of this optimal design, we obtained a theoretical normalized second-harmonic conversion efficiency $\eta$ of 0.56% ${\mathrm{W}}^{-1}{\mathrm{cm}}^{-2}$, calculated by [25,38]

B. Experimental Setup

Figure 2 shows the experimental setup used to characterize the SHG conversion and photon-pair generation. Light was coupled in and from the chip by two pairs of grating couplers. The directional couplers are placed between the main waveguide and grating couplers on both sides for multiplexing or demultiplexing light of different wavelengths, which also realize the mode conversion between the ${\mathrm{TM}}_0$ mode in the input/output grating couplers and the ${\mathrm{TM}}_2$ mode in the main waveguide. The coupling losses including directional coupler are 9.2 dB at 1560.4 nm and 14.9 dB at 780.2 nm. The propagational loss of a 5-mm-long waveguide is about 0.9 dB mainly from fabrication disorders.

 

Fig. 2. Experimental setup to characterize the SHG conversion and photon-pair generation. (a) Second-harmonic generation measurement. EDFA, erbium-doped fiber amplifier; FPC, fiber polarization controller; PD, photodetector. (b) Correlated photon-pair measurement. LPF, long-pass filter; SNSPD, superconducting nanowire single-photon detector; TCSPC, time-correlated single-photon counter. (c) Time-energy entanglement measurement. (d) Heralded single-photon detection.

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In SHG measurement as shown in Fig. 2(a), a continuous-wave tunable semiconductor laser in the 1560 nm wavelength region (Yenista Tunics-T100S-HP) was used as a pump source, and output light near 780 nm wavelength was sent into a highly sensitive photodetector for measurement. In the SPDC measurement as shown in Figs. 2(b)–2(d), the pump light in the 780 nm wavelength region was from a tunable diode laser (Newport Velocity TLB-6700). The generated photons and the pump laser were collected at the other side of the waveguide and then separated by two long-pass filters. The rejection ratio of the filters is larger than 120 dB, and they added about 2.0 dB loss to the generated photon pairs. Then the photon pairs were split by a 50/50 splitter before being sent to two channels of the superconducting nanowire single-photon detectors (SNSPDs). The detection efficiencies of the A, B, and C channels are approximately 30%. In Fig. 2(b), the output signals were sent directly to time-correlated single-photon counter (TCSPC) for characterizing temporal correlations. Figure 2(c) shows the experimental setup for measuring two-photon interference. The light is sent into a free-space Franson interferometer after the long-pass filters. A piezo-based phase shifter in the interferometer is used to tune the phase between the long path and short path. The measurement setup for the heralded single photon is shown in Fig. 2(d). Channel A works as a route to detect heralding photons. We measured the double coincidences of channels AB, AC, and triple coincidences of channels ABC.

3. RESULTS AND DISCUSSION

A. Biphoton Coincidence

The internal pair generation rate (PGR) describes the pair flux on chip, excluding any loss in the measurement. Here, to obtain PGR, we first calculated the second-order self-correlation function $g^{(2)}$ for SPDC [3,39],

 

Fig. 3. (a) One sample data series of single count rates $C_{\mathrm{A}}$ and $C_{\mathrm{B}}$ of two detector channels A and B in 1 min time. (b) Coincidence counts per minute. The coincidence time window ${\tau }_{\mathrm{w}}$ is 3 ps. (c) Second-order correlation function $g^{(2)}(\tau )$ of generated photon pairs. The circles are the normalized $g^{(2)}$ function calculated from measured coincidence count rates with Eq. (2), and the solid line is the fitted $g^{(2)}$ function from Eq. (3).

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Next, we fit measured $g^{(2)}(\tau )$ function to the following formula:

With this fitting method, we calculated and plotted the internal PGR versus on-chip pump power in Fig. 4(a), with a fitted slope of approximately 6.68 MHz/mW. Our device achieved an internal rate of MHz level when the input power was below 0.1 mW. The largest internal PGR observed was around 3.46 MHz for a 0.42 mW on-chip pump power. The corresponding detected coincidence histogram is shown in Fig. 4(b).

 

Fig. 4. (a) On-chip pair generation rate (PGR, units of MHz) versus pump power (units of mW) in the waveguide. The error bars are one standard deviation in each direction. (b) Time-bin coincidence histogram detected for a 0.42 mW on-chip pump power. (c) Coincidence-to-accidental ratio (CAR) versus PGR. The data in this figure are measured in Fig. 2(b).

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The coincidence-to-accidental ratio (CAR) quantifies the signal-to-noise ratio of the photon-pair source. Figure 4(c) shows the measured CAR versus the internal PGR. The CAR value was calculated from the normalized signal-idler second-order cross-correlation function $g_{\mathrm{fit}}^{(2)}(t)$ [3,39] using the equation $\mathrm{CAR}=g_{\mathrm{fit}}^{(2)}(t)-1$. The highest CAR value 5773 was measured at a PGR of 1.07 MHz. As expected, the CAR decreased at higher pair generation rates. We also used $\mathrm{CAR}\propto 1/\mathrm{PGR}$ to fit the CAR data and show the fitted curve in Fig. 4(c), which means that CAR is inversely proportional to PGR.

B. Photon Interference

We conducted a two-photon interference experiment to confirm the time-energy entanglement properties of the generated photon pairs [16]. The experimental setup is depicted in Fig. 2(c). In this interference experiment, there are four possible scenarios for the two photons. If both photons take either the shorter or the longer path, a central peak will appear in the coincidence histogram at zero delay. However, if the two photons take different paths, two side peaks will emerge because they are distinguishable due to the additional phase delay imposed by the piezo phase shifters. The coincidence histograms at different phases are shown in Figs. 5(a)–5(c), as expected. The circles of Fig. 5(d) show the normalized coincidence as a function of phase, and the fitted sinusoid curve shows a visibility of 94%. This violates Bell’s inequality, surpassing the limit of 70.7% [40]. The visibility did not reach 100% primarily because the free-space Franson interferometer was not phase stabilized and was subject to environmental disturbances which introduced noise. The red and blue diamonds related to right axis of Fig. 5(d) show the single photon counts measured at the corresponding detector channels versus the phase, so the possibility of first-order interference is also excluded from this figure.

 

Fig. 5. (a)–(c) Coincidence histograms over 1 min for different interferometric phases with the corresponding phases noted in (d). (d) The left axis shows the normalized coincidence counts versus the phase. The visibility of the raw data yields 94%. The right axis shows the single counts measured at the corresponding phase. The data in this figure are measured in Fig. 2(c).

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C. Heralded Single-Photon Source

Single-photon sources play a crucial role in quantum-enhanced technologies, and the heralding of single-photon states is a method of generating probabilistic single photons, where the detection of one photon heralds the existence of its twin photon [41,42]. Figure 2(d) shows the experimental setup of measuring heralded single photons. We recorded the coincidence events between the heralding channel and the other two channels, as well as the coincidence events involving all three channels. Using the normalized self-correlation equation [14] $g_{\mathrm{H}}^{(2)}(0)=N_{\mathrm{ABC}}{N}_{\mathrm{A}}{(2N_{\mathrm{AB}}{N}_{\mathrm{AC}})}^{-1}$, the measured value at a 0.35 mW on-chip power is calculated to be 0.174, well below the classical threshold. The difference between our value and that from the typical etched PPLN device [14] is primarily attributed to the utilization of a larger coincidence time window. This adjustment was necessary to compensate for the imperfect symmetry of the 50/50 splitter. It also helps to generate nonzero triple coincidence events when the detected raw coincidence value is low due to the loss. This experiment verifies that our device can serve as a reliable heralded single-photon source.

D. Result Discussion

Here, we mainly discuss the effect of loss on the PGR in the experiment. As we discussed before in Section 3.A, from Eq. (3), we extracted the maximum value of internal PGR, $R_{\mathrm{pair}}=3.46\mathrm{MHz}$ when the on-chip power was 0.42 mW. In the experiment, the measured coincidence rate $R_{\mathrm{AB}}$ at this power was 81 Hz. The difference between the coincidence rate and fitted PGR is due to the loss in the optical path from the device to the single-photon detector. On one hand, if we consider overall loss in the optical path which we have also mentioned in Section 2.B in the measurement setup, including fiber-to-chip loss of 9.2 dB at 1560.4 nm, filter and collimators’ loss of 2.0 dB, 50/50 splitter loss, and 30% detectors’ efficiency, the on-chip PGR is approximately 0.62 MHz, and it will rise to 0.94 MHz when considering a propagation loss of 0.9 dB in the waveguide. On the other hand, if we directly use the equation $R_{\mathrm{pair}}=C_{\mathrm{A}}{C}_{\mathrm{B}}/2R_{\mathrm{AB}}$ [14] to calculate the internal PGR, the result will be 3.78 MHz, which is very close to the fitted value.

Finally, we will estimate the PGR theoretically. For an unfiltered case in the SPDC process, the estimated PGR [43,44] is

4. Conclusion

In conclusion, we have experimentally demonstrated entangled photon-pair generation at telecommunication wavelengths with BICs on an etchless platform. Our device, which does not require poling or etching, produces a pair generation rate of 6.68 MHz/mW, comparable to that of state-of-the-art devices. We also performed a detailed loss analysis of PGR in the device. The pair generation rate can be further improved by reducing the effective modal area and enhancing the spatial overlap between the two modes in the nonlinear region. This can be achieved by using a material with a higher refractive index for the waveguide, by adopting an LNOI wafer with a thicker LN layer, or by introducing periodic poling to the LN thin film [34]. The coupling efficiency can also be improved by changing the grating coupler to the edge-coupling method to get larger raw counts of photons. Considering that we have previously demonstrated some high-performance classical integrated optical devices on the same BIC platform [27,30], the potential for realizing integrated quantum photonics on the BIC platform is very promising. The availability of a photon-pair source opens up new possibilities for quantum photonic circuits on this hybrid etchless platform. Additionally, this hybrid etchless platform is expected to facilitate the development of other new high-${\chi }^{(2)}$ materials for possible use in integrated quantum photonics.