Generation of entangled photon pairs from a silicon bichromatic photonic crystal cavity

Integrated photonics has emerged as the platform of choice for several quantum technologies. The ability to fabricate many different devices on the same chip, using the same well-established technology developed for microelectronic circuits,¹ allows for functionalities that are otherwise unattainable, despite being fundamental for the implementation of many quantum information protocols.² 

The generation of nonclassical states of light through suitably engineered photonic devices plays a pivotal role in quantum photonic applications. In particular, these are the devices in which entanglement, a genuine quantum property, is created typically. In integrated photonics, sources of entangled photon pairs typically rely on spontaneous nonlinear light–matter interaction, which is enhanced by resonant structures.^3–8 In particular, spontaneous four-wave mixing (SFWM) is the process of choice for silicon and silicon-based devices, in which an intrinsic third-order nonlinear susceptibility exists.

Several different types of resonant structures can be employed to efficiently enhance SFWM.⁹ Among these, whispering gallery mode resonators, such as rings, microtoroids, or microspheres,^10–12 naturally fulfill the energy conservation and phase-matching requirements, at least in the wavelength ranges in which waveguide dispersion can be neglected. However, these choices typically entail large modal volumes, while the generation efficiency scales as a power of the ratio between the resonance quality factor and the effective confinement volume, Q/V.³ The same is not true for standing-wave resonators. Photonic crystals (PhCs) and, particularly, photonic crystal cavities can serve as a tool to confine light in a diffraction-limited mode volume while keeping large Q-factors,^13,14 thus exhibiting nearly optimal Q/V ratios at a given wavelength. On the contrary, in fully confined geometries, the phase-matching condition is replaced by the mode overlap for standing waves, and energy conservation is not trivially met.^15–17 In this work, we experimentally show how silicon photonic crystal cavities fabricated in a fully CMOS-compatible platform can be engineered to obtain a high-brightness integrated source of pure time-energy entangled photon pairs. By exploiting evenly spaced high-Q resonances obtained in the quasi-harmonic potential of a silicon bichromatic photonic crystal cavity,^18,19 we hereby engineer the whole integrated chip, including input/output sub-wavelength grating couplers, access waveguides, and photonic crystal input/output waveguides coupled to the targeted bichromatic cavity, which allows us to efficiently excite the pump resonance and extract the generated signal and idler frequencies. Despite the intrinsic presence of two-photon absorption in silicon, which might have hindered the actual detection of quantum effects in devices with such small confinement volumes, we experimentally demonstrate the emission of photon pairs with an estimated generation efficiency as high as $∼11.7$ MHz/mW² and a measured on-chip emission rate up to 120 kHz. In addition, to showcase the suitability of our device for applications in photonic quantum technologies, we perform an experiment showing that the spontaneously generated photon pairs are, indeed, time-energy entangled, by assessing a Bell’s inequality violation by more than five standard deviations in a Franson interferometry configuration.²⁰ The latter represents the first experimental demonstration of time-energy entangled photons from a single photonic crystal cavity in a pure silicon membrane.

The device developed in this work consists of a single, multi-mode photonic crystal cavity with a bichromatic potential design, which was originally proposed in Ref. 18 and later demonstrated in different material platforms, such as silicon^19,21 and III/V alloys.^22,23 This type of a resonator was soon recognized to display a harmonic-like effective confinement potential that results in a spectrum of high-quality factor modes,²² which was then exploited to demonstrate the first optical parametric oscillator based on a photonic crystal resonator²³ as well as highly efficient parametric fluorescence in the InGaP platform.²⁴ In our implementation of such “bichromatic cavity,” we start from a line defect in a triangular lattice of circular air holes with lattice constant a, in which an entire row of holes with a reduced radius is shifted by half a period, and its lattice constant a′ is slightly mismatched with respect to the one of the surrounding lattice. In fact, we impose their ratio to follow the relation a′/a = N/(N + 1), where N represents the number of periods a′ inserted in the cavity region before matching the lattice of the surrounding photonic crystal, a. The aperiodic distribution of the dielectric constant in the cavity region acts as an effective parabolic potential for photons [Fig. 1(a)] such that the energy levels (viz., the localized cavity modes) in the photonic bandgap are arranged in a way that mimics the behavior of a quantum harmonic oscillator. Hence, nearly equally spaced resonances are obtained, with small deviations due to the non-perfect parabolicity of the effective potential.²² 

Here, in the perspective of device integration, we presented a sample to be measured with in-plane transmission/reflection spectroscopy, exploiting input/output access waveguides that are evanescently coupled to the central resonator, as shown in Fig. 1(b). Thus, the entire chip layout was designed to allow for input/output fiber coupling through sub-wavelength grating couplers,²⁵ yielding simpler experimental coupling schemes compared to previous studies on similar platforms.^7,26 Such single-etch grating couplers convey light to standard ridge silicon-on-insulator (SOI) waveguides, which become suspended before transitioning to W1.05 or W1.3 photonic crystal waveguides (i.e., standard line defect in a triangular lattice whose width is increased by a factor of 1.05 or 1.3, respectively). We estimated approximately 8 dB of insertion losses per grating coupler. The larger insertion losses reported here as compared to Ref. 25 may be attributed to propagation losses due to stitching defects in the coupling ridge waveguide. As it is evident from Fig. 1(b), the input/output coupling is symmetric with respect to the cavity center, and the evanescent coupling is engineered through numerical simulations by 3D finite-difference time-domain (FDTD) as a function of the horizontal and vertical distances of the waveguide ends from this center, parameterized by n_x and n_y periods of distance from it.

The spectral characterization of the devices typically yields a comb-like multimode structure in either reflection or transmission.^19,22 In particular, we are able to assess up to nine resonances in a single device. The statistics of the relative detuning among the first three triplets are summarized in Fig. 2. Here, δΔ_ijk = ν_k + ν_i − 2ν_j is the detuning from the triply resonant (i.e., equal frequency spacing) condition for triplets of adjacent resonances. The average detuning is within 25 GHz for the three triplets examined, with a standard deviation of 60 GHz, on average. Despite the bichromatic cavity approximating a harmonic oscillator, it is challenging from a technological point of view to achieve perfect energy matching in the fabricated device, especially when dealing with high-Q resonances. Of the adjacent triplets of 54 cavities, 13 triplets have an FSR lower than 10 GHz, and only three of those are lower than 5 GHz. From this systematic characterization, we selected a device with nearly equally spaced resonances, shown in Fig. 1(c), corresponding to a bichromatic PhC cavity with parameters N = 48, a = 400 nm, n_x = 4, and n_y = 5, respectively. A Lorentzian fit of the spectral line shape of each resonance transmission gives Q-factors for signal, pump, and idler as high as Q_s ≃ 50 000, Q_p ≃ 90 000, and Q_i ≃ 65 000, respectively. In contrast, from the dip visibility in the reflection spectra, the coupling efficiency can be estimated to be η_s = 0.62, η_p = 0.42, and η_i = 0.93 for the signal, pump, and idler modes, respectively. The reflection signal is modulated by Fabry–Pérot (FP) interference fringes that most probably originate from reflections between the output grating coupler and the high impedance interface between the ridge waveguide and the PhC waveguide. To estimate the visibility of the reflection dips, we have fitted the spectra with a heuristic model, i.e., a combination of a sinusoidal function for the FP fringes and a Fano line shape for the cavity mode resonance, from which the visibility is extracted. By tuning the laser on-resonance, we estimated an overall chip insertion loss of α_s = 11.6 dB, α_p = 11.5 dB, and α_i = 8.5 dB, respectively, between the input and output fibers. The bichromatic design ensures that the resonances are nearly evenly spaced, on average. For the case of the device measured in this work to probe entangled photon pair generation, we quantify the detuning δΔ_spi = 9.5 GHz, which is larger than the average linewidth of the resonances, $δν̄=3.5$ GHz. This detuning certainly plays a detrimental role, lowering the overall efficiency. In fact, the overall efficiency is proportional to the symmetric overlap integral of the resonances with respect to the pump frequency,^23,27 i.e., $ρint∝∫Lp2(ωp)Ls(ωp+Ω)Li(ωp−Ω)dΩ$⁠, which, for the triplet hereby considered, is approximately two orders of magnitude smaller than the perfectly matched configuration.²⁸ Nevertheless, as shown in Sec. III, this is enough to show the spontaneous generation of signal/idler pairs and it does not hinder the observation of time-bin entanglement with a relatively high efficiency, thus leaving a large room for improvement by exploiting post-fabrication tuning processes to achieve an even better energy matching.¹⁹ 

Here, we report the quantum photonic performances obtained from the device whose transmission spectrum is shown in Fig. 1(c). As already mentioned, the selected cavity exhibits a good trade-off between relatively low insertion losses and a detuning of 9.5 GHz for the first triplet.

Figure 3 shows a complete scheme of the experimental setup. In order to measure time correlations, the interferometer section is bypassed. The input laser (EXFO T100S-HP) is used to pump the spontaneous process. A narrowband tunable passband filter (Santec OTF-350) is used to filter out the laser-amplified spontaneous emission. Two fiber arrays polished at the angle required by the grating design (18°) are used for in-coupling and out-coupling. At the output of the sample, the pump is suppressed via a Bragg filter tuned to the pump wavelength rejecting 35 dB, and then, the entangled pair is separated and spectrally filtered with free-space tunable bandpass filters (Semrock). The signal and idler photons are then routed to two independent superconducting nanowire single-photon detectors (SNSPDs) to measure temporal correlations between the arrival times [Fig. 4(a)]. By studying the dependence of the integrated coincidence peak as a function of the pump power, we retrieved the expected quadratic dependence, as shown in Fig. 4(b). We do not observe any complex behavior in the generation trend due to the thermo-optic contribution acting as a differential tuning of the resonances of the targeted triplet, as observed, e.g., in other material platforms.^23,29 Multiple factors may play a role in this respect. Because of the higher thermal conductivity of silicon, the inhomogeneity of the spatial thermal profile is less severe than, for example, in Ref. 23, so all the resonances shift rigidly and the triplet alignment is less affected. Moreover, because of the non-negligible detuning of this particular triplet, the main energy-matching contribution comes from the tails of the Lorentzian line shapes; hence, we are less sensitive to an eventual detuning.

Compared to integrated photon pair sources based on traveling wave resonators,^33–35 our device displays a footprint of only 230 μm², which benefits from the extreme confinement capability of the PhC localization mechanism. Furthermore, the use of a multimode cavity results in more compact and easier-to-design resonators than the PhC cavity solutions demonstrated so far,^7,36–38 which relied on coupled resonators or dispersion-engineered PhC waveguides, in terms of both device footprint and mode volume. In terms of performance, our device displays a normalized generation efficiency comparable to previous results obtained in silicon PhC cavities.⁷ Despite the larger frequency detuning in the present case, our device exhibits a 20-fold improvement in generation efficiency compared to previous results based on micro-ring resonators with comparable quality factors.³⁵ 

Despite these advantages, our source suffers from several extrinsic limitations that currently hinder the full potential of our approach. In particular, the statistic deviation from the triply resonant condition still obliges to compromise between quality factor (and, therefore, field enhancement) and generation efficiency, as the employment of narrower resonances reflects under tighter spectral alignment conditions. Specifically, the device presented here suffers from a deviation of 9.5 GHz (about 2.7 linewidths), which we estimate to reduce the maximal generation efficiency by approximately one order of magnitude.²³ On the one hand, this issue could be mitigated by further improving the fabrication; for example, advanced techniques have demonstrated PhC cavities with Q factors exceeding 10⁷.¹⁴ On the other hand, the detuning issue could be addressed by implementing post-fabrication fine-tuning techniques, for example, laser-assisted local oxidation of the silicon membrane,¹⁹ which were proven capable of fully recovering the triply resonant condition for small values of initial detuning. Finally, while the purpose of this work included proving the compatibility with the silicon photonics platform, we remark that the presence of two-photon absorption ultimately poses a limitation to the maximum pump power in our device. In this perspective, silicon nitride, silicon oxynitride, and silicon carbide materials represent good CMOS-compatible alternatives, albeit the lower performance when compared to silicon devices. A promising alternative platform is provided by some III/V alloys, which, in general, benefit from a higher nonlinear coefficient and from a pump-induced tuning mechanism that allows reaching an almost perfect energy-matching condition.^23,24 Net pair generation rates exceeding 10 MHz and an internal efficiency of 16 GHz/mW² have recently been reported.²⁴ The lack of two-photon absorption limits the pump power only by higher-order emission, ultimately resulting in the emergence of parametric oscillations.²³ However, it is well known that III/V alloys encounter several challenges related to CMOS compatibility, which limit their potential for the development of scalable integrated devices. In summary, we have shown here a micrometer-scale footprint, highly efficient source of entangled photon pairs realized in integrated silicon photonics technology. By leveraging the mature CMOS-compatible fabrication, this demonstration opens a pathway toward the engineering of highly compact and power-efficient quantum devices, a crucial aspect in the perspective of large-scale integration of multi-component, complex quantum devices.^35,39–41

M.C., T.P., A.M., D.G., T.F., and M.G. acknowledge support by the EU H2020 QuantERA ERA–NET co–fund in Quantum Technologies Project CUSPIDOR co–funded by the Italian Ministry of Education, University and Research (MIUR) and by the Austrian Science Foundation FWF under Project No. I 3760–N27. M.G. acknowledges support from the Italian Ministry of Research (MUR) through the grant “Dipartimenti di Eccellenza” 2018–2022 (Grant No. F11I18000680001). M.L. acknowledges PNRR MUR project “National Quantum Science and Technology Institute” – NQSTI (Grant No. PE0000023). A.B. and D.B. acknowledge funding from the Hyper–Space project (Project ID No. 101070168), co–funded by the EU and the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors thank Alma Halilovic and Stephan Bräuer for cleanroom and other technical support. We thank A. De Rossi and A. Chopin for useful scientific discussions.

The authors have no conflicts to disclose.

Andrea Barone: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Visualization (lead); Writing – original draft (lead). Marco Clementi: Investigation (supporting); Writing – original draft (supporting); Writing – review & editing (equal). Thanavorn Poempool: Resources (equal); Writing – original draft (supporting). Alessandro Marcia: Investigation (equal); Methodology (supporting). Daniele Bajoni: Methodology (equal); Supervision (equal); Writing – review & editing (equal). Marco Liscidini: Funding acquisition (equal); Project administration (equal); Writing – review & editing (equal). Dario Gerace: Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Thomas Fromherz: Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Matteo Galli: Investigation (equal); Methodology (equal); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.