Photonic device and classical measurements

As sketched in Fig. 1a, our silicon chip integrates several building blocks towards realizing a stand-alone quantum photonic device: a ring resonator (RR), a PF based on multi-mode cascaded Bragg filter (BF), and modal couplers, as well as in and out grating couplers. The quality factor and the free spectral range (FSR) of the RR are equal to Q = 3 × 104 and 200 GHz around 1535 nm, respectively. As shown in Fig. 2a, the transmission profile of our RR features by design a frequency-comb structure matching that of the two first telecom channel pairs (see Methods for the design and the fabrication). This makes it possible to use off-the-shelves telecom components for demultiplexing and routing the information out of the chip. Through spontaneous four-wave mixing (SFWM), photon pairs are created according to the conservation of both the energy and the momentum. The photon pairs are produced in a symmetrical way with respect to the pump wavelength (Fig. 2a, b). In the following, long-wavelength photons are referred to as signal photons, whereas short-wavelength ones to as idler photons. Concerning the PF, the grating period of the BFs has been chosen to reflect light around 1535 nm into the second-order mode (see Methods). By adding a single-mode waveguide between the sections of the PF, the second mode is radiated into the substrate, breaking the coherence that would otherwise have been established. This strategy allows to implement high-rejection filters being all-passive, thanks to the cascading of modal-engineered Bragg gratings with relaxed fabrication requirements28.

Fig. 1: Schematics of the experimental setup. a Input laser with associated filter (TF) rejecting the amplified spontaneous emission and a polarization controller (PC). Laser light is injected in the ring resonator (RR) through the grating coupler and then propagates to a modal coupler (MC) and through the integrated pump filter (PF). b Schematic top view of one of the cascaded Bragg filter (BF) composing the PF. The output of the chip is connected to either a coincidence setup (c) with a beam splitter (BS) and bandpass filters to demultiplex signal and idler photons (TF signal/idler) or to the entanglement qualification setup (d) in a folded-Franson configuration. e Spectrum of the signal and idler filters, which exhibit 22 dB and 25 dB rejection for the two-FSR shift and three-FSR shift configurations, respectively. Full size image

Fig. 2: Transmission spectrum of the circuit. a Scan of the output port of the chip and the feedback port, which represents the portion of light reflected by the first section of the filter. The filter exhibits a rejection of 60 dB (limited by the noise floor of the detector). b Zoom over the pumped resonance of the ring. As can be seen, it corresponds to the center of the pump filter and its 3 dB bandwidth is 42 ± 0.5 pm. Signal, idler, and pumped resonances used in the experiments are highlighted, in red the two-FSR shift, blue the three-FSR shift, and green being the pumped resonance. Full size image

A modal coupler is added between the ring and the first Bragg section to recover part of the reflected light through the feedback port32. This makes the alignment of the pump laser to the desired resonance easier even with thermal drift. It is noteworthy that no cladding is added to improve the natural transverse magnetic (TM) polarization filtering of the waveguide. Finally, subwavelength fiber-chip grating couplers are employed to inject and extract transverse electric (TE) polarized light using standard single-mode optical fibers33.

Prior to quantum qualification, we characterize the circuit in the classical regime by measuring its transmission spectrum using a tunable laser associated with a data acquisition system (Yenista Tunics and CT400) (Fig. 2). We use a polarization rotator to inject TE-polarized light into the grating. The pump-rejection filter has a 3 dB bandwidth of 5.5 nm. In our case, the usable bandwidth is only 3 nm, as only the deepest part of the filter can be exploited for the rejection of the pump. As shown in Fig. 2, the measured rejection of the filter is higher than 60 dB (dark-blue curve), which corresponds to the noise floor (red dashed line) of our detector. This measured rejection rate is consistent with state-of-the-art realizations for single-chip PF16,17,18. To further investigate the performances of the PF, we need to qualify the entangled states generated on an advanced integrated circuit including this PF.

Time correlation measurements

We proceed to time correlation measurements as a prerequisite to two-photon interference for qualifying the amount of entanglement carried by the photon pairs generated and filtered on chip. To reveal time correlation (Fig. 1c), signal and idler photons are separated and sent to different detectors that are connected to a time-to-digital converter (TDC). The statistics in the arrival times and related delays is then recorded and reconstructed as a coincidence histogram (Fig. 3a). To this end, the paired photons are demultiplexed at the chip’s output with off-the-shelf filters of only 22 dB cross-talk (as shown in Fig. 1e). The pump is set to λ p = 1534.2 nm (C-band) with an input power of 2.8 mW after the polarization controller (Fig. 1a). As a first step, we study the closest resonances from the pump, i.e., paired channels distant by two- and three-FSR, as they may suffer preferably from the pump photonic noise. The related wavelength for the two- and three-FSR shift are highlighted in Fig. 2 and detailed in the Methods. Examples of typical coincidence histograms are shown in Fig. 3a, where distinct coincidence peaks emerge over a small background of accidental counts. This stands as a clear signature of the simultaneous emission of the photon pairs. The width of the coincidence peak is given by the convolution of the coherence time of the photons σ coherence ~ 110 ps, of the detectors’ timing jitters σ jitter ~ 100 ps, and of the time resolution of the TDC σ resolution ~ 1 ps. The full width at half maximum of the coincidence peak is about 160 ps, which is consistent with \(\sqrt{{\sigma }_{\mathrm {coherence}}^{2}+{\sigma }_{\mathrm {jitter}}^{2}+{\sigma }_{\mathrm {resolution}}^{2}} \sim 150\ {\rm{ps}}\). Both the two-FSR shift and three-FSR shift resonances exhibit similar results.

Fig. 3: Recorded coincidence histograms. a The histograms represent the recorded coincidences for both two-FSR shift and three-FSR shift resonances. The overall integration time is 10 s and the measurements are done with SSPD detectors (Fig. 1b). The two-FSR rate is of about 116 counts/s with an SNR of 67.5, whereas the three-FSR coincidence rate is of about 151 counts/s with a SNR of 100. The noise level within the peak is between 1.5 counts/s and 1.7 counts/s. b The histograms represent the coincidences at the output of the interferometric setup sketched in Fig. 1c for the two-FSR shift resonances. They show a maximum and a minimum of interference (region (1)). Here, the overall integration time is of 5 s. The error bars for all points come from Poissonian statistics associated with the pairs (e.g., \(\sqrt{N}\), N being the number of coincidences). It is noteworthy that similar histogram are obtained for the three-FSR shift case. Full size image

We now consider the internal brightness of the ring (Table 1). The overall losses of the setup, including the input/output and propagation losses of the chip, are outlined in Table 2 of the Methods section. The single count rates in the coincidence experiment are of 4 × 104 signal counts per seconds and 3 × 104 idler counts per seconds, with 17 dB and 18.5 dB of losses, respectively. The overall coincidence peak spreads over several time bins and shows an average of 120 coincidences per second over a time window of 400 ps (Fig. 3a). With all those figures, we can infer an internal generated photon-pair rate of (2.1 ± 0.2) × 106 pairs/s. As the ring shows resonances of 42 pm width (Fig. 2b) and the power in the ring is estimated to be 0.9 mW, we estimate an internal brightness of ~500 pairs/s/mW2/MHz. Due to the non-deterministic wavelength separation induced by the beam splitter (Fig. 1a) and the spectral filtering ensured by the bandpass filters in each arm, the rate at the output of the chip is 4 times higher, i.e., about 480 pairs generated per second for each channel pair. Let us stress that this coincidence rate stands among the best values reported for photonic devices embedding several key components7,20,34,35,36,37,38. In comparison, similar realizations suffer from low coincidence rates due to prohibitive losses, precluding any further analysis of entanglement19,20. It is noteworthy that the other interesting feature reported in Table 2 is the 2 dB loss for the PF, which is almost only due to propagation. This low value associated with a high-rejection level and a narrow bandwidth makes our pump-filtering strategy a promising candidate for next-generation quantum photonic circuits.

Table 1 Summary of the losses experienced by the paired photons. Full size table

Table 2 Summary of signal and idler wavelengths. Full size table

Before addressing entanglement analysis, a relevant figure of merit associated with time correlation measurements consists in evaluating the signal-to-noise ratio (SNR) between the coincidence peak and the background noise. In the measurements presented in Fig. 3a, the SNR is >60 for both histograms (2-FSR shift and 3-FSR shift). Accidental counts mainly come from successive pair events, when one of the two photons has lost its paired companion. This SNR can be improved by using a lower pump power at the price of reduced coincidence counts and of longer integration times39. There, our strategy is slightly different and promotes pragmatic realizations of QIS experiments by emphasizing high-coincidence counts, while keeping a moderate but safe SNR9.

Energy-time entanglement analysis

The photon pairs are genuinely energy-time entangled, as they are produced by SFWM15,40,41,42,43,44,45,46. Entanglement is analyzed using a folded-Franson arrangement consisting of an unbalanced fiber Michelson interferometer (F-MI) (Fig. 1d)23,47. A piezo-transducer is used to extend the fiber in one arm, changing the imbalance of the interferometer, and thus the relative phase between the two arms. Energy-time quantum correlation are revealed by the coherent superposition of the contributions coming from identical two-photon paths (short–short and long–long) contrarily to the contributions coming from different paths (long–short, or conversely). Consequently, a coincidence histogram with the emergence of three peaks is recorded9 (Fig. 3b). The central peak gathers the two indistinguishable contributions leading to interference, provided all experimental conditions reported in the Methods section are satisfied. The total and average numbers of coincidences in the central and side peaks, respectively (Fig. 3b) are used to plot the patterns shown in Fig. 4.

Fig. 4: Plots of the coincidence rates (blue curve) for the central (Region (1) in Fig. 3b) and the average of the side peaks (Regions (2) and (3) in Fig. 3b). Each point is obtained with a 5 s integration time and the step increment of π/8. The side peak rates show the stability of the measurement. Here, noise counts are not removed from the measurements, (a) corresponds to the two-FSR shift resonances with a noise of 0.5 counts/s, (b) is the three-FSR shift resonances with a noise of 0.9 counts/s. The error bars for all points come from Poissonian statistics. Full size image

Interference patterns recorded for two-FSR shift (Fig. 4a) and three-FSR shift (Fig. 4b) resonances are obtained with a phase resolution of \(\frac{2\pi }{20}\), compliant with the F-MI stability. The interferometer π-dephasing timescale is in the hour range, which leaves enough time to perform a scan without being subjected to detrimental phase drifts. The side peak in Fig. 3b also shows the stability of the photon generation process. The typical acquisition time for recording two fringes is 6 min. The noise figure in the central peak is of about 0.5 and 0.9 counts/s for the two-FSR shift and three-FSR shift resonances, respectively. The two-photon interference fringes are fitted with respect to N 0 (1 − V cos(2ϕ)), where N 0 is the mean number of coincidences and V the fringes visibility considered as a free-fit parameter to infer the visibility. Raw visibilities of (98.0 ± 2)% and (96.7 ± 3)% without subtraction of photonic or detector noise are obtained, for the two-FSR shift pairs (R2 of 0.96) and for the three-FSR shift pairs (R2 of 0.99), respectively. The net visibility is obtained by subtracting photonic noise originating from the detectors’ dark counts (200 counts/s) and corresponds to (99.6 ± 1.5)% and (98.0 ± 1.2)% for the two-FSR shift and three-FSR shift pairs, respectively.

We extend our investigations according the same methodology for subsequent paired channels within the S-band and the full C-band30. More precisely, we explore the entanglement quality of 9 extra paired channels, i.e., up to 11-FSR shift, spaced by 40 nm (1515–1555 nm) on both sides of the pump channel, leading to the ability of supporting a high number of users in a multiplexing scenario (Table 2)9. The details for the signal and idler wavelengths corresponding to i-FSR shift, with 2 ≤ i ≤ 11, are reported in the Methods. The raw visibilities for all the paired channels exceeds 92% for an internal rate ≥1 MHz as shown in Fig. 5.

Fig. 5: Raw and net visibilities and internal rate plotted as a function of the signal and idler wavelengths. For sake of clarity, we associate signal and idler wavelengths to their corresponding telecom band. Full size image

It is noteworthy that two other photonic noise contributions have been evaluated before being neglected: multiple photon-pair events and non-perfect overlap between the two identical two-photon paths (“short–short” and “long–long”). The former was not considered because of the low mean number of photon pairs per gate window (\(\bar{n}=3\,\times\,1{0}^{-4}\)). The origin of the latter contribution lies in the wavelength difference between the signal and the idler over the full range of analysis (~50 nm), leading to potentially slightly distinguishable “short–short” and “long–long” two-photon paths. The time arrival difference has been evaluated to be <10−5 ps, whereas the full width at half maximum of the coincidence peak is equal to 160 ps (Fig. 3a), which represents several orders magnitudes higher than the shift between the “short–short” and “long–long” path.

This result not only stands as among the highest raw quantum interference visibility for time-energy entangled photons from a micro/nanoscale integrated circuit over such a large spectral window (partially over the S-band and fully over the C-band) but also the first entanglement qualification of a complex integrated circuit including the PF7,36,48. Furthermore, generating genuinely a pure maximally entangled state from an integrated source associated with high-coincidence rates will be of special interest for QIS experiments.