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Abstract
The silicon nitride (Si3N4) platform, demonstrating a moderate third-order optical nonlinearity and a low optical loss compared with those of silicon, is suitable for integrated quantum photonic circuits. However, it is challenging to develop a crack-free, wafer-scale, thick Si3N4 platform in a single deposition run using a subtractive complementary metal-oxide-semiconductor (CMOS)-compatible fabrication process suitable for dispersion-engineered quantum light sources. In this paper, we demonstrate our unique subtractive fabrication process by introducing a stress-release pattern prior to the single Si3N4 film deposition. Our Si3N4 platform enables 950 nm-thick and 8 μm-wide microring resonators supporting whispering-gallery modes for quantum light sources at 1550 nm wavelengths. We report a high photon-pair generation rate of ∼1.03 MHz/mW2, with a high spectral brightness of ∼5×106 pairs/s/mW2/GHz. We demonstrate the first heralded single-photon measurement on the Si3N4 platform, which exhibits a high quality of conditional self-correlation gH(2)(0) of 0.008 ± 0.003.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The generation of photon pairs and heralded single photons commonly exploits nonlinear optical processes such as second-order spontaneous parametric down conversion (SPDC) and third-order spontaneous four-wave mixing (SFWM). The complementary metal-oxide-semiconductor (CMOS)-compatible materials such as silicon, silicon nitride and silicon oxynitride can generate single photons through SFWM. The quantum light sources can be integrated with passive silicon photonic linear optical components such as beam splitters [1], channel filters [2] and delay lines [3] for quantum information processing on a single chip [4,5]. The CMOS materials have the advantage of leveraging the mature CMOS fabrication process, which is ready for manufacturing integrated photonic chips in a foundry. While other on-chip platforms for quantum technologies such as quantum dots and color centers are not compatible with the CMOS process. Thus, the integrated silicon photonics provides a good platform for quantum technologies.
Silicon nitride stands out as a suitable platform for photonic integration, due to its low intrinsic linear loss and low nonlinear two-photon absorption loss in the telecommunication bands (1550nm/1310nm) because of the wide bandgap of ∼5 eV while having a refractive index of ∼2.0 for good optical confinement. Stoichiometric silicon nitride (Si3N4) deposited by low-pressure chemical vapor deposition (LPCVD) contains a low concentration of H-bond that is responsible for absorption losses at ∼1520 nm. Researchers have demonstrated an ultra-low waveguide propagation loss of < 1 dB/m [6] and a high quality (Q) factor in the order of 107 for Si3N4 microring resonators [6–9]. The low loss enables the demonstration of time-bin entanglement circuits with a 14cm-long unbalanced Mach-Zehnder interferometer utilizing a double-stripe Si3N4 waveguide with a propagation loss of 0.2 dB/cm [10].
Photon pairs can be generated from Si3N4 using pump-degenerate SFWM, where two degenerated pump photons are annihilated while one signal and one idler photon at generally different frequencies are created. The generated signal and idler frequencies are equally spaced around the pump frequency following energy conservation. However, the spontaneous process is weak as it is excited by the vacuum fluctuation.
High-Q microresonators with a strong cavity enhancement can enhance the weak SFWM process. Researchers demonstrated time-bin entangled [11] and frequency-bin entangled [12] photon sources using Si3N4 microrings. Resonators supporting whispering-gallery modes (WGMs) that avoid the scattering losses from the cavity inner sidewall potentially enable higher Q factors than microrings that exhibit both inner and outer sidewall scattering losses.
Figure 1(a) schematically illustrates the use of a waveguide-coupled wide-width Si3N4 microring supporting WGMs as a quantum light source. Dispersion engineering for Si3N4 microresonators is required to align the pump and the generated signal-idler photon pairs to three nearly equally spaced cavity resonances, especially for high-Q resonators with a narrow cavity linewidth (< hundreds of MHz) that is comparable to the dispersion-induced deviations (∼few MHz) from equal cavity mode spacing, as illustrated in Fig. 1(b). A near-zero dispersion is preferred to attain an efficient photon-pair generation for a wide-span quantum frequency comb [13].
Fig. 1. (a) Schematics of photon-pair generation through a pump-degenerate SFWM process in a wide-width microring resonator supporting WGMs on a Si3N4-on-silica platform. Inset: the energy level diagram for the SFWM process. (b) Schematics of the cavity-enhanced SFWM process in the frequency spectrum considering the effects of the cavity dispersion and the pump detuning.
For microresonators supporting WGMs such as microdisks and wide-width microrings, a Si3N4 thickness of exceeding 800 nm is required to realize a near-zero dispersion when pumping at ∼1550nm wavelengths [14]. However, fabricating such a thick Si3N4 platform is challenging due to the large tensile stress of the Si3N4 film that will form cracks (typically for a thickness > 400 nm) [15,16].
The reported subtractive fabrication processes including our prior work make use of temperature cycling that requires two steps of Si3N4 film deposition [6,8,9,17,18], which is likely to introduce an additional layer of silicon oxynitride in between the two Si3N4 layers. With manually applied trenches along the wafer rim to stop any cracks initiated at the wafer rim from penetrating inward (defining a crack-free region), researchers demonstrated a 950nm-thick Si3N4 film [19]. While with etched trenches, researchers only demonstrated Si3N4 film thicknesses of up to 750 nm [8,9]. Other researchers developed the wafer twist-and-grow approach to achieve a crack-free Si3N4 film on 8” wafers, with a demonstrated Si3N4 film thickness of only up to 800 nm [17]. However, the reported subtractive processes cannot achieve a near μm-thick Si3N4 film deposited in a single growth. The manually applied trenches are not feasible in a foundry line.
The photonic Damascene process that employs a stress-release pattern in an additive fabrication process can achieve a Si3N4 film thickness of 1.5 μm in a single deposition run [20,21]. However, the integral chemical-mechanical polishing (CMP) step, which is likely to cause non-uniform removal rates locally (for different geometries) and globally (at different positions on the wafer) may not be suitable for fabricating devices with a larger variation in geometry such as waveguide-coupled mm-sized microdisks. Only waveguide-based structures with widths of a few μm have been demonstrated.
In this work, we further develop our subtractive Si3N4 fabrication process reported in [18]. By introducing a stress-release pattern prior to the Si3N4 film deposition, we achieve a 950nm-thick, crack-free Si3N4 film in a single deposition run using CMOS-compatible subtractive processes on 4” wafers [22]. Our fabrication process without using CMP enables flexibility in the device geometry design, featuring waveguide-coupled wide-width microrings in this work and waveguide-coupled mm-size disks in our previous work [18]. Our wafer-scale process is developed using a standard CMOS fabrication line without manual steps or electron-beam lithography, which can be transferred to a silicon CMOS foundry. Thus, our platform is potentially suitable for large-scale photonic integration with dispersion-engineered integrated quantum light sources.
Using our Si3N4 WGM wide-width microrings for quantum light sources, we demonstrate the photon-pair and heralded single photon generation. Our 61.5μm-radius and 8μm-wide microrings, with a typical loaded Q-factor of ∼1×106, demonstrate a photon-pair generation rate of ∼1.03 MHz/mW2, with spectral brightness of ∼5×106 pairs/s/mW2/GHz that is comparable with the state-of-the-art. We study the heralded single-photon property with the conditional self-correlation measurement, which reveals a low conditional self-correlation gH(2)(0) of 0.008 ± 0.003. To our knowledge, this is the first heralded gH(2)(0) measurement in the Si3N4 platform.
2. Device fabrication
We develop a fabrication process for crack-free, μm-thick Si3N4 devices based on wafer-scale subtractive processes using a 4’’ CMOS fabrication line. The fabrication starts with coating silicon wafers with a 3.3μm-thick thermal oxide as the lower-cladding layer. We use i-line photolithography (ASML 365nm stepper) for pattern definition, with a field size of 15 mm × 15 mm and a reduction ratio of 5. Prior to the Si3N4 film deposition, we pre-pattern a stress-release pattern on the oxide layer with C4F8/H2/He-based etchants with a depth of ∼1.5 μm, which exceeds the targeted Si3N4 film thickness (Fig. 2(a)). The stress-release pattern comprises quasi-periodic alternate rows of squares and of 45°-rotated squares arrays. The square element size is ∼5 μm. The edge-to-edge distance between alternate rows is ∼11.5 μm.
Fig. 2. Schematics of the fabrication process flow for crack-free μm-thick Si3N4 devices based on a wafer-scale subtractive process. Steps (a) and (b) in the dashed-line box are the key steps employed in the process.
We then deposit the Si3N4 film with a thickness of up to 950 nm using LPCVD at ∼780 °C in a single deposition run. This is followed by a ∼700nm-thick low-temperature oxide (LTO) layer as an etching hard mask, as illustrated in Fig. 2(b). We leverage the LTO to prevent the extension of cracks typically initiated at the wafer rim due to wafer-handling into the stress-release pattern.
We pattern the Si3N4 devices using the i-line stepper. The minimum coupling gap spacing is limited to ∼400 nm. We etch the LTO hard mask and the Si3N4 subsequently using C4F8/H2/He- and SF6/C4F8-based etchants, respectively, as illustrated in Fig. 2(c).
We use high-temperature annealing to minimize the H content in the Si3N4 devices to minimize absorption in the ∼1520nm wavelengths. However, the annealing also introduces a large tensile stress to the Si3N4 film. To minimize wafer bowing, we remove the backside Si3N4 film before the annealing (Fig. 2(d)).
We perform O2 annealing for 0.5 hour followed by N2 annealing for 3∼5 hours upon 1150 °C (Fig. 2(e)). By oxidizing the sidewall of the devices through the O2 annealing, we smoothen the sidewall with an additional buffered oxide etchant (BOE) etch. We note that for microdisks, which contain a larger built-in strain than waveguides, both the annealing and the BOE etch in step (e) may roll up the devices. Thus, we skip step (e) when processing microdisks.
We deposit a layer of LTO as the upper-cladding layer (Fig. 2(f)). This is followed by another high-temperature annealing to further drive out the H content from both the LTO cladding and the Si3N4 devices. Finally, we expose the waveguide end-facet through deep-trench etching, with a depth of ∼150 μm for lensed fiber end-coupling.
Figure 3(a) shows the picture of the wafer with a 950nm-thick Si3N4 film and the LTO cladding (at process step (b)) under a green-light illumination. The photolithography region with the stress-release pattern is crack-free.
Fig. 3. (a) Picture of a 4” silicon wafer under a green-light illumination after the deposition of Si3N4 and of an LTO hard mask. Cracks are only noticeable in the wafer rim region outside the photolithography region. (b) Colored SEM image of a waveguide-coupled microring surrounded by the stress-release pattern. Inset i: Colored SEM images of the cross-sectional view of the waveguide-microring coupling region.
Figure 3(b) shows the colored scanning electron micrograph (SEM) of a waveguide-coupled 115μm-radius microring with a width of 2 μm (at process step (c)). The device is surrounded by the stress-release pattern with a spacing of >20 μm between the device and the pattern. The inset i shows the cross-sectional view for a waveguide-coupled microring at the coupling gap region, after depositing the upper-cladding layer (at process step (f)). Due to the loading effect of the oxide etchant during the patterning of the hard mask, a Si3N4 slab layer is formed in the coupling region. The LTO upper-cladding layer with a poor conformality forms an air-void in the coupling region, which can cause extra scattering losses.
3. Device characterization
3.1. Experimental setup
Figure 4 schematically illustrates the experimental setup for characterizing the Si3N4 microresonators for quantum light source properties. We use a continuous-wave (c. w.) wavelength-tunable laser in the 1550nm wavelengths (Santec TSL-510) as the pump laser. We use an erbium-doped fiber amplifier (EDFA) connected to a variable optical attenuator (VOA) to control the pump power. We use one 0.3nm-bandwidth tunable band-pass filter and three 200GHz dense-wavelength-division multiplexing (DWDM) filters (at channel 26) to suppress the amplified spontaneous emission (ASE) noise from the EDFA, with a total extinction ratio of ∼200 dB. We use a polarization-maintaining (PM) lensed fiber to launch the transverse magnetic (TM)-polarized light into the device. We monitor the power at the fiber tip by a photodiode (denoted as PD1) connected to the 1% arm of the fiber coupler (before the DWDM filters). We collect the output-coupled light using another PM lensed fiber. We cascade four DWDM filters as notch filters with a total extinction ratio of ∼60 dB to reject the residual pump light. We monitor the residual pump power through the pass-port of the notch filters using a power meter (PD2). We separate the signal and the idler by a demultiplexer (DMUX), followed by three DWDM filters separately on channels 22 and 30 to attain another ∼200dB noise suppression.
Fig. 4. Schematics of the experimental setup for measuring the quantum light source properties of the SFWM-generated photon pairs. We modify the detection ports for measuring (a) the cross-correlation, (b) the self-correlation for the signal photons, and (c) the heralded single photons using the idler photons for heralding. (d) Schematic cross-sectional view for the device under test. PC: polarization controller, TBPF: tunable band-pass filter, PD: photodiode, CH: channel, P: pass-port, R: reflection-port.
We detect the idler and signal photons by the two channels (CH1 and CH2) of the superconducting nanowire single-photon detector (SNSPD) system (Single Quantum). The detection efficiencies for CH1 and CH2 are 85% and 88%. We connect the SNSPDs to a time-to-digital convertor (TDC) (quTAG) to record the photon arrival time. The smallest timing resolution is 1 ps. For measuring the pair-generation rate (PGR) and the cross-correlation of photon pairs, we record the timing delay histograms between the two SNSPDs. We use an active feedback-controlled power-locking scheme (within transmitted pump-power fluctuations of ∼0.5 dB monitored at PD2) to lock the pump laser wavelength to a cavity resonance. The pump is locked on the blue side of the measured cavity resonance close to the dip.
Figure 4(d) schematically illustrates the cross-section of a waveguide-coupled microring device under test (DUT). The microring width is ∼8 μm and the outer radius is ∼61.5 μm (measured to the microring outer sidewall). Such a wide-width microring supports low-radial-order WGMs. The characterizations for the linear optical properties of the DUT follow our previous work [18] and the results are detailed in Supplement 1. For the quantum light source measurements, we pump at the TM1 mode with a loaded Q-factor of ∼1×106 centered at ∼1556.4 nm, which is within the 200GHz-DWDM channel 26. We measure the photon-pair generation at the adjacent FSRs (l = ±1) from the pump (l = 0). The DUT reveals a cavity dispersion D2/2π of ∼11.1 ± 1.1 MHz (corresponding to a waveguide chromatic dispersion D of ∼65 ps/nm/km) for TM1 mode. The insertion loss at the pump wavelength is ∼4.8 dB. We assume an input-fiber coupling loss of ∼3.3 dB at the end-facet for estimating the input pump power. We extract the output-coupling loss to be ∼1.5 dB from our PGR measurements below (Sec. 3.2). Our cavity dispersion measurement suggests that the operation wavelength range of our device for l = ±1 can be within 1500 nm ∼ 1620 nm, where we obtain for the TM1 mode cavity dispersion of <20 MHz that is smaller than the cavity linewidth.
3.2. Characterization of the PGR
We model the pump-degenerate SFWM process considering both the cavity dispersion and the cross-phase modulation (XPM) (see the details in Supplement 1). We express the PGR inside the cavity as:
where R (in Hz/mW2) is the PGR per squared pump power, Pin is the pump power at the input waveguide, l is an integer (= ±1, ±2, …) that denotes the relative azimuthal mode order away from the pump cavity frequency (at l = 0), κ (in rad/s) is the average total loss rate for the signal (κl) and the idler (κ-l), g0 = n2cħω02/(n02Veff) is the FWM gain parameter, N0 is the pump photon number inside the cavity, Al = (σ - D2l2/2 + 2g0N0) represents the overall frequency detuning for modes ± l, including the pump frequency detuning σ (= (ωp – ω0), where ωp is the pump-laser frequency, ω0 is the cavity resonance for the pump), the second-order dispersion term -D2l2/2 and the XPM term 2g0N0, n2 is the nonlinear refractive index, n0 is the effective refractive index, and Veff is the effective mode volume. Here, we assume l > 0, with l denoting the signal and –l representing the idler. The term g0N0 gives the third-order nonlinear parametric gain in angular frequency units. The N0 depends linearly on Pin and the cavity enhancement.With σ = -g0N0 (ωp < ω0,), we can attain the maximum pump photon number inside the cavity N0,max = (4κe,0/κ02)·(Pin/ħω0), where κe,0 is the external coupling loss rate for the pump cavity mode (l = 0) and κ0 is the total loss rate for the pump cavity mode (detailed in Supplement 1). Upon such a pump power, we have Al = (-D2l2/2 + g0N0) for modes ± l. The corresponding maximum PGR per squared pump power is given as:
From Eq. (2) we estimate the R, assuming κl ∼ κ-l ∼ κ ∼ 2π×200 MHz, κ/2 >> Al, and thus the denominator (κ2+4Al2) ∼ κ2, n2 = 1.4 ∼ 2.4×10−19 m2/W [23–25], ω0 ∼ 2π ×193 THz, Veff ∼7.5×10−16 m3, n0 ∼ 1.9, κe,0/κ0 = ηe,0 ∼ 0.48, where Veff and n0 are from numerical simulations, κ and κe,0 are extracted from curve fitting of the resonance lineshapes, as shown in Supplement 1, Figs. S7(a)-(c). We estimate R to be 1.2∼3.8 MHz/mW2.
In the case that the pump power is well below the optical parametric oscillation (OPO) threshold, i.e. the SFWM gain is much lower than the cavity loss where 2g0N0 << κ±l, the pump-degenerate SFWM generated photon-pair flux depends quadratically on the pump power.
The simultaneously generated signal and idler photon-pairs are correlated in time. Here, we investigate the photon-pair flux at the output waveguide. We express the photon-pair density |C(tl, t-l)|2 out-coupled to the waveguide at a delay time between the signal time tl and the idler time t-l as:
Due to the cavity lifetime τc = 1/κ, the delay time between the emitted photon pairs exhibit a double exponential relation centered at Δt = 0, given by Eq. (3). Integrating Eq. (3) over the entire Δt span, we obtain the emitted photon-pair flux as ηe,lηe,-l·RPin2, where ηe,±l = κe,±l/κ±l is the waveguide extraction efficiency for the ± l modes.
The photons experience linear optical losses from the chip to the single-photon detectors. The detected SFWM-generated single-photon flux (either the signal or the idler) by the SNSPD is given as η±l·RPin2, where η±l denotes the total loss of the system for the signal or idler photon, including the out-coupled waveguide extraction efficiency (ηe,±l), the output-fiber coupling loss, the fiber and filter losses, and the SNSPD detection efficiency. The SNSPDs have receiver noise, mainly contributed by the broadband Raman noise (denoted as n±l·P, with n±l the noise coefficient) from the fiber and the chip that linearly depends on the pump power, and by the dark counts from the SNSPDs (denoted as d±l). Thus, the single-photon flux p±l at each SNSPD is given as,
The SFWM process generates signal and idler pairs at various ± l modes while we only detect one photon-pair at a time for a particular pair of ± l modes. We use subscripts s and i to replace l and -l to denote the corresponding signal and idler detection channels.
Figure 5(a) shows the measured pump-power dependence of the on-resonance count rates at the signal and idler channels. We apply quadratic fits following Eq. (4) to extract the quadratic terms for both channels, with the fitted ηiR = 53947 ± 3374 Hz/mW2 for CH1 and the fitted ηsR = 48506 ± 2961 Hz/mW2 for CH2. We only consider low pump powers of < 1 mW for the curve fitting. Our curve fits suggest a large linear noise coefficient n of 21138 ± 2494 Hz/mW for CH1 and of 14933 ± 1871 Hz/mW for CH2. Figure 5(a) illustrates the fitted quadratic and linear contributions. The fits suggest dark counts d of ∼212 Hz for CH1 and of ∼137 Hz for CH2, which are consistent with the measured dark counts of 184 ± 21 for CH1 and 65 ± 12 for CH2.
Fig. 5. Power dependence of the (a) on-resonance count rates with quadratic fits and (b) off-resonance count rates with linear fits. The dotted and dashed lines in (a) indicate the contributions from the quadratic and linear terms, respectively. (c) Coincidence spectrum upon a pump power of ∼0.3 mW measured by the TDC with a time bin of 40 ps. (d) Power dependence of the coincidence and accidental count rates. The window for integrating the count rates is indicated by the shaded region in (c). The coincidence rates are fitted with only the quadratic term.
Figure 5(b) shows the measured pump-power dependence of the off-resonance count rates at CH1 and CH2, which suggest the combined fiber Raman noise (with the pump-photons essentially remained in the input-waveguide) and the dark counts. We apply linear fits, with the fitted n of 5172 ± 46 Hz/mW for CH1 and of 4156 ± 51 Hz/mW for CH2. The fitted d is ∼272 Hz for CH1 and ∼211 Hz for CH2.
We attribute the linear terms of the off-resonance counts to the upstream delivery fiber with a length of ∼1.3 m (after the DWDM filter till the input lensed fiber). While we attribute the linear terms of the on-resonance counts to the same fiber and to the Si3N4 microresonator. Thus, we attribute the extra linear contribution of ∼15966 Hz/mW (consider CH1 as an example) to the microresonator, which is ∼3× larger than the fiber Raman noise. Our analysis suggests the spontaneous Raman noise in the Si3N4 microresonator is ∼1000× higher than that in the 1.3m-long silica fiber as follows: Given the cavity enhancement factor (= (4κe,0νFSR)/κ02, νFSR is the FSR in frequency) for the pump frequency is ∼540, and the effective mode area Aeff for TM1 mode is ∼2 μm2, we estimate assuming a 1mW pump power at the input-waveguide the pump intensity I inside the cavity is ∼270 mW/μm2. With a round-trip length L of ∼386 μm, the intensity-length product I·L is ∼104 W/μm. While the pump power inside the fiber is ∼3.3dB above the pump power in the input-waveguide. With an Aeff of ∼78 μm2 for a singlemode fiber, we estimate the pump intensity in the fiber is ∼0.027 mW/μm2. The I·L is 3.6×104 W/μm in the 1.3m-long fiber. We believe the linear noise is related to the Raman noise, because the Raman spectrum for amorphous silicon nitride shows broadband emission below 1000 cm-1 [26]. Operating at the anti-Stokes side and at a reduced on-chip temperature can be possible ways to reduce the Raman noise.
The TDC records the coincidence between the signal and idler photons arriving at the two SNSPD channels at times ts and ti. Figure 5(c) shows an example of the coincidence count rate recorded upon a pump power of ∼0.3 mW. The exposure time is 480 s. The count rate expressed as psi·dΔt is the number of recorded counts within a time bin dΔt of 40 ps divided by the exposure time, where psi(Δt = ts - ti) = η'sη'i|C(Δt)|2 + ps·pi is the joint probability density at the TDC (η’ = η/ηe is the total loss ratio excluding the waveguide extraction efficiency for the signal or idler photons). The double exponential distribution of the coincidence count rate is centered at a systematic relative fiber-optic delay. The fitted τc is ∼0.77 ns. The accidental counts ps·pi·dΔt that do not record the arrival of photons in pairs contribute to the noise floor.
The coincidence counts are given by ηsηi·RPin2, accounting for the total loss at both the signal and idler channels. Upon a range of pump powers of 0.047 ∼ 3.7 mW, we chose exposure times of 10 ∼ 6300 s to accumulate a reasonable level of accidental counts. We extract the coincidence rate by integrating the overall count rate within a window covering all the coincidence events, subtracting the accidental rate within the same window, as indicated in Fig. 5(c). We obtain the accidental rates by averaging the count rates outside the coincidence window. We include the standard deviation of the overall counts assuming a Poisson distribution. The standard deviations for the accidentals are from the noise-floor counts. Figure 5(d) shows the count rates for the coincidence and accidental rates upon various pump powers. By applying a quadratic fit with only the quadratic term to the coincidence rate, we obtain the coefficient ηsηiR = 2547 ± 64 Hz/mW2.
We obtain the PGR through the fitting of single and coincidence count rates R = ηsR· ηiR/ ηsηiR = 1.03 ± 0.09 MHz/mW2.
The spectral brightness (in pairs/s/mW2/GHz) of a photon-pair source is given as R normalized by the average linewidth of the signal and idler resonances. With a measured resonance linewidth of ∼201 MHz for the signal channel and of ∼209 MHz for the idler channel, our source demonstrates a spectral brightness of 5×106 pairs/s/mW2/GHz. Using Eq. (1) and assuming negligible dispersion and phase-modulation ((κ2+4Al2) ∼ κ2), we estimate the g0N0 from our device to be ∼10.3 MHz/mW×Pin.
We extract the total loss of the system, with ηi (= ηiR/R) = 12.8 ± 0.5 dB and ηs (= ηsR/R) = 13.3 ± 0.5 dB. We only need to estimate the input-coupling loss. We consider the idler channel as an example. The total loss comprises a waveguide extraction efficiency of ∼4.3 dB (extracted from the resonance fitting), a measured total fiber loss of ∼6.4 dB, a SNSPD detection efficiency of ∼0.7 dB (according to the equipment specifications) and the fiber output-coupling loss (to be estimated). Thus, we estimate the fiber output-coupling loss to be ∼1.4 ± 0.5 dB.
We measure the CAR given as the coincidence counts divided by the accidental counts within the same window. Figure 6 shows the measured CAR as a function of pump power. We apply a coincidence window corresponding to twice the cavity lifetime, 2τc, as shown in the inset of Fig. 6. Upon the minimum pump power of ∼0.047 mW, we attain the highest CAR of 1864 ± 571. The error bar is one standard deviation propagated from the overall counts and the accidental counts, dominated by the accidental counts. We calculate the orange curve in Fig. 6 from the fitted coincidence rate and single rates assuming a coincidence window of 2τc, following the theoretical modeling in Supplement 1, Eq. (S36).
Fig. 6. Measured power dependence of the CAR. The curve is calculated from the quadratic fits shown in Figs. 5(a) and (d). Inset: the shaded region defines the coincidence counts window.
3.3. PGR at various l modes
We measure the PGR values at various l modes to evaluate the frequency span for the DUT. We extract the PGR values at modes l from 1 to 7 by detecting the photon flux power dependence at only the signal channel. Figure 7(a) schematically illustrates the experimental setup at the downstream modified from the setup shown in Fig. 4. We apply the C-band programmable filter (Finisar WaveShaper 4000A) centered at the resonance frequencies with a bandwidth of 100 GHz. We use two tunable bandpass filters with a total extinction ratio of ∼70 dB to further reduce the noise. We detect the signal photons using SNSPD CH1.
Fig. 7. (a) Schematics of the experimental setup at the downstream for measuring different l modes at a single channel. (b) Measured pump-power dependence of the count rates for different l modes shown with quadratic fits (lines). (c) Extracted PGR values at different l modes (grey bars) and theoretical values (colored bars).
Figure 7(b) shows the measured power dependence of the count rates for different l modes with quadratic fits. We extract the PGR with the fitted ηlR from the quadratic term using Eq. (4). We fixed the d = 184 Hz (the measured dark counts) for these fittings while the linear and quadratic terms are orders of magnitude larger than the d term.
We estimate the total loss ηl for different l modes as discussed in Section 3.2. The extracted R values for different l modes are shown in Fig. 7(c) indicated by the grey bars. The colored bars in Fig. 7(c) show the theoretically estimated values using Eq. (1). We adopted the corresponding values of κl, κ-l and Al extracted from the transmission resonance spectrum for each mode l. The g0N0 value adopted in the calculation is inferred from the measurement of R as detailed in Section 3.2. Generally, the R value reduces with l due to the cavity dispersion that misaligns the signal (idler) frequencies from the corresponding cavity resonances.
For specific resonances, we remark that the PGR can be compromised by a local modulation of the cavity dispersion. For example, we note a smaller measured PGR at l = 4 compared to the theoretical expectation. We attribute this to a scattering-induced mode splitting observed at l = -4, with a peak-to-peak separation of ∼300 MHz (see Supplement 1 for the transmission spectrum).
3.4 Cross-correlation and self-correlation
We measure the second-order correlation g(2) between two intensities (photon numbers) to reveal the quantum states of the light. We direct the two intensities of interest to two separate single-photon detectors and measure the statistics of the counts over the delay time between the two detectors. The cross-correlation studies the correlation between two different photon components. The self-correlation measures the correlation of a single photon component separated by a beam splitter.
In the following, we neglect the overall detuning Al for as l = 1, which satisfies κ/2 >> Al . We express the second-order correlation for signal and idler photon-pairs at the detection ports as:
The detected single-photon flux ps and pi (in Eq. (4)) include the SFWM-generated flux (η·RPin2) and the noise.
Figures 8(a), (b) show the cross-correlation upon pump powers of (a) ∼0.47 mW and (b) ∼0.93 mW, with gsi(2)(0) of 929 ± 19 and 377 ± 7, respectively. We adopted a time bin dΔt of 160 ps. The solid curves indicate the theoretical values calculated from Eq. (5). The dashed curves indicate the theoretical values without the noise contributions. With considering the noise we adopted the ps and pi values including the linear noise and the dark counts. Without considering the noise we only included the quadratic terms, where gsi(2)(0) has a power dependence of 1/Pin2. Upon low pump powers, the gsi(2)(0) is largely compromised by the linear noise.
Fig. 8. (a)(b) Cross-correlation of the signal and idler photons upon pump powers of (a) ∼0.47 mW and of (b) ∼0.93 mW. The symbols are the measurements. The curves are the theoretical calculations from the fits shown in Fig. 5. The solid line includes noise contributions. The dashed line assumes no noise contributions. (c)(d) Self-correlation of (c) the signal photon and (d) the idler photon upon the pump power of ∼1.5 mW. The symbols are the measurements. The curves are the fits.
We measure the self-correlation using the setup as illustrated in Fig. 4(b). We split either the signal photon or the idler photon into two paths using a 50:50 fiber-coupler, which is connected to two SNSPD channels one at each port. Figures 8(c), (d) show the measured self-correlation g(2)(Δt) for (c) the signal photon and (d) the idler photon upon a pump power of ∼1.5 mW. We used a time bin of 160 ps.
We obtain the self-correlation g(2)(Δt) through normalizing the overall counts by the average accidental counts away from the zero delay. The signal channel shows a measured gss(2)(0) of 1.96 ± 0.13. The idler channel shows a measured gii(2)(0) of 1.82 ± 0.11. The self-correlation values for the signal and idler photons exhibit similar profiles. Both the measured gss(2)(0) and gii(2)(0) are consistent with g(2)(0) = 2 for a single-mode thermal state.
Assuming κl ≈ κ-l ≈ κ, we express the self-correlation as [27] g(2)(Δt) = 1+(1+κ|Δt|/2)2exp(-κ|Δt|), where g(2)(0) = 2. We adopted this expression for the fitting. The fitted κ/2π is ∼310 MHz. The distribution is broader than the exponential shape by an additional quadratic term (1+κ|Δt|/2)2. We provide a possible explanation for the broader self-correlation function. The cross-correlation function shows a double exponential decay corresponding to the photon lifetime of a simultaneously generated signal and idler photon pair. While for the self-correlation, the |Δt| reveals the emission time difference of the single photon component, which contains the statistic information of the photon emission from a thermal process. As long as the cavity has a finite lifetime and the emission time of the single photon component is not simultaneous, the self-correlation will be broader than only the double exponential decay.
3.5. Heralded single photons
The single-photon generation through SFWM only shows the single-photon property of anti-bunching upon the detection of the heralding (trigger) photon. In this section, we study the heralded single-photon property by measuring the conditional second-order correlation for the signal photons when detecting the idler photon as the herald.
We express the second-order correlation for the heralded single photons at zero delay (Δt = 0) as [28]
where Nssi is the number of triple coincidence counts, Nsi is the number of dual coincidence counts, and Ni is the number of idler counts. We obtain the number of counts through post-processing the time-tag values. We adopted a time bin of ∼1.46 ns, corresponding to 2τc.The experimental setup for the heralded single-photon measurement is shown in Fig. 4(c). We chose the idler photon as the trigger detected by a single-photon avalanche detector (SPAD) (IDQ ID230). We split the signal photons into two paths and detect by two SNSPDs for self-correlation measurements. We operate the TDC (IDQ ID800) in the time-tag mode that registers the arrival times of three detection channels. The timing resolution is ∼81 ps. We chose seven different pump powers of 0.19 mW, 0.47 mW, 0.93 mW, 1.5 mW, 1.9 mW, 2.3 mW, and 3 mW. The corresponding exposure times are 441 min, 384 min, 57.9 min, 10.3 min, 14.1 min, 11.6 min, and 6.6 min.
Figure 9(a) shows the measured gH(2)(Δt) for heralded single-photons upon a pump power of ∼3 mW, which shows anti-bunching at zero delay (Δt = 0, δt2 ∼ 7.6 ns) of 0.087 ± 0.010. Away from the coincidence window, we obtain the measured gH(2)(Δt) ∼ 1.0. We extract gH(2)(0) over various pump powers, as shown in Fig. 9(b). The error bars are mainly contributed by the rare triple-coincidence events. We measure the lowest gH(2)(0) = 0.008 ± 0.003 upon a pump power of ∼0.47 mW.
Fig. 9. (a) gH(2) as a function of delay time Δt under a pump power of ∼3 mW. (b) Measured gH(2)(0) upon various pump powers. The symbols are the measurements. The curves are the theoretical modeling calculated from the fitted single rates and coincidence rate shown in Fig. 5. The solid curve accounts for the noises. The dashed curve only considers the SFWM contribution.
The conditional self-correlation is related to the cross-correlation as [29] gH(2)(0) = (2/gsi(2)(0))·(2-1/gsi(2)(0)). By adopting a coincidence window of 2τc, we have gsi(2)(0) = 1+CAR ≈ CAR. The solid curve in Fig. 9 is derived from the calculated CAR shown in Fig. 6. The dashed line in Fig. 9 shows the modeled power dependence of gH(2)(0) without the noise contribution, following gH(2)(0) ≈ 4aPin2 -2a2Pin4 (a = 2Rτc/(1-e-1)) (detailed in the Supplement 1).
4. Discussion and summary
In summary, we have demonstrated an integrated quantum light source using Si3N4 WGM microring resonators through SFWM. Table 1 summarizes the comparison among other silicon-based quantum light sources using SFWM. Our devices show a high pair-generation rate R of 1.03 MHz/mW2 and a high spectral brightness of 5×106 pairs/s/mW2/GHz compared with devices demonstrated from other Si3N4 platforms. We have demonstrated a low conditional self-correlation of 0.008 ± 0.003 upon a pump power of ∼0.5 mW, which is the first heralded g(2) measurement in the Si3N4 platform to our knowledge.
Table 1. Comparison among silicon-based integrated quantum light sources
Due to the smaller third-order nonlinearity of Si3N4, the PGRs for the Si3N4 microresonators are two to three orders of magnitude lower than that of the Si platform. However, as a material platform for integrated quantum circuits, the Si3N4 platform is advantageous in terms of a lower linear loss and a lower nonlinear loss and thus has a better scalability. Compared to the Hydex platform with third-order nonlinearity that is smaller than that of the Si3N4, the PGR is three orders of magnitude lower than that of Si3N4. For the double-stripe Si3N4 waveguide, since a large fraction of the waveguide mode overlaps with silica of a lower third-order nonlinearity, the PGR is two orders of magnitude lower than that of thick Si3N4 waveguides. In addition, such a waveguide is operating in the normal dispersion region with a large chromatic dispersion D of ∼-590 ps/nm/km.
We have included in the Supplement 1 the statistics of intrinsic Q-factor values Q0 for different device designs from various dies on multiple wafers. Our 61.5μm-radius and 8μm-wide microrings have revealed a high Q0 of 1.6×106 for TM1 mode, and of 2.6×106 for TE1 mode. We extract the corresponding waveguide attenuation [8] to be ∼0.26 dB/cm for TM1 mode and ∼0.15 dB/cm for TE1 mode.
We have demonstrated a wafer-scale Si3N4 subtractive fabrication process that enables integrated quantum light sources. The process is supported by the standard CMOS fabrication line. We have grown up to a 950nm-thick Si3N4 film in a single deposition run by introducing a stress-release pattern at the under-cladding oxide layer.
Funding
Research Grants Council, University Grants Committee (16202615, 16203317).
Acknowledgments
We thank the Nanosystem Fabrication Facility (NFF) of the HKUST for device fabrication and helpful discussions.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available from the corresponding authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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