In quantum key distribution (QKD)^[1–4], single-frequency lasers are widely used as a light source to generate weak coherent states (WCSs). Going beyond point-to-point QKD, large-scale quantum networks with many users and simultaneous communication links require multi-frequency light sources and wavelength-division multiplexing (WDM) technology to improve communication performance and efficiency. As a direct solution for integrated QKD transceiver chips^[5], combining multiple lasers with different wavelengths is experimentally feasible; however, it has substantial challenges in scalability.

In recent years, the development of manufacturing processes of compact chip-scale microring resonators (MRRs)^[6] has provided a more efficient way to acquire highly coherent multi-frequency light such as the dissipative Kerr soliton (DKS) comb^[7], of which the formation is governed by a double-balance of nonlinearity and dispersion, as well as dissipation and gain. The distinctive compact^[8], low-noise^[9], and low-power comsumption^[8,10] frequency comb has emerged as a promising light source for a range of technologies^[11], including optical clocks^[12], optical frequency synthesis^[13,14], classical communication^[15–18], and sensing^[19,20]. The advent of the optical frequency comb has enabled the provision of a diverse and abundant single-frequency resource with a highly coherent property. The DKS can generate a single optical comb with a high signal-to-noise ratio (SNR) across a broad band (150 nm), encompassing both C and L bands^[21–24]. The combination of an optical comb with WDM technology represents a crucial step toward the integration and scalability of multi-user quantum networks^[25]. The indistinguishability of independent light sources belonging to different users is essential for measurement-device-independent QKD (MDI QKD)^[26–28], which is based on two-photon Hong–Ou–Mandel (HOM) interference^[29,30]. Therefore, obtaining high-visibility HOM interference between frequency lines generated from different independent MRRs is highly desirable.

Despite progress in frequency locking fields such as the f-2f^[31,32] and atomic reference schemes^[33], which can achieve frequency stability of $9.5\times {10}^{-14}$ at 1 s^[34], it remains challenging to attain a high degree of homogeneity across all comb lines of two independent DKS combs. This challenge arises from the differences between independent MRRs due to fabrications. Considering the free spectral range (FSR) of the microring in the first-order approximation of dispersion, $\mathrm{FSR}(v)=c/n_g\times L$, even minor discrepancies in the length of the cavity ($L$) or imperfections in the waveguide can result in a deviation of the FSR.

In this work, we generate two independent DKS combs from different dispersion-engineered silicon-nitride MRRs simultaneously, and 10 high-SNR comb lines are successfully obtained with WDM. For each DKS comb generation system, the auxiliary laser-assisted intracavity thermal balance technique^[35–37] and temperature control have been employed to enhance the overall stability, sustaining operation for over 8 h with two free-running lasers^[38]. The integration of micro-ring heaters on the chip and the single-sideband (SSB) modulator has been employed to eliminate the frequency differences of the combs at several FSRs away from the pump. Additionally, high-speed modulators chop continuous light into ultra-narrow pulses with a width of about 0.4 ns. Finally, we demonstrate the HOM interference between 10 independent comb lines and obtain high visibility between them. The results show the great potential of DKS combs as quantum communication network light sources.

The experimental setup is illustrated in Fig. 1. The optical comb light source is based on an integrated silicon nitride platform (Ligentec AN800) comprising two micro-resonator devices with identical cavity design parameters. Two tunable semiconductor lasers are used as main pump sources, and a single-frequency laser with a narrow linewidth serves as the auxiliary laser applied to heat the micro-resonator from the opposing direction, which is based on the dual-driven technique^[36–38] for stably generating the DKS comb. The light polarization on the chip is set to the transverse electric (TE₀₀) mode, which exhibits higher loaded quality factors and extinction ratios. The employment of WDM fiber filters combines light from different pump channels into erbium-doped optical amplifiers (EDFAs), which are configured to enhance the light power to compensate for optical path and coupling losses. Two cascaded three-port circulators are used to implement a dual-driven soliton access system. Power meters (PMs) and photodetectors (PDs) are used to record changes in the power spectrum of the pump and the soliton comb, respectively, which help determine the soliton-step position. Simultaneously, the optical spectrum analyzer records the frequency spectrum of the corresponding soliton states.

The implementation of dense wavelength demultiplexing (DWDM) and a 32-channel arrayed waveguide grating (AWG) filters the residual pump light, thereby isolating the micro-cavity frequency comb with a 100 GHz frequency spacing. Here, we use high-precision frequency translation with SSB modulation, combined with the on-chip micro-heater, to align the frequencies between different DKS comb lines.

At this stage, the two overlapping spectral signal photons are directed to the subsequent encoding apparatus. A commercial intensity modulator splits continuous-wave light from a single DKS comb line into a series of narrow pulses. The electrical signals driving the intensity modulators (IMs) are generated by an arbitrary waveform generator. A variable optical attenuator (VOA) attenuates the pulses to the single-photon level for two-photon HOM interference measurements.

We use optical and electrical packaging [see Fig. 2(a)] to accommodate the silicon nitride chip, which is located at the center of the chip holder and features an inverted taper design to enhance the coupling of light into and out from the chip. It is then coupled to the ultra-high numerical aperture (UHNA7) fiber array. The coupling point between the chip and the optical fiber array is fixed with UV-curable glue (see the dark part of the image), which ensures the long-term stability of the system coupling after high temperature aging. The printed circuit board (PCB) is designed to extend the electrical port for the on-chip micro-ring heaters using gold and soft wires, with the final exportation located at the other end. The submount provides support for the chip temperature control system, enabling the transfer of heat generated by the operational chip through the oxygen-free copper to the cooling sheet for thermal feedback.

A self-made wavelength calibrated system based on an asymmetric Mach–Zehnder interferometer (AMZI) is used to record over 100 resonant frequencies of the TE₀₀ mode, from which the cavity group velocity dispersion (GVD) is extracted using the equation ${\omega }_{\mu }={\omega }_0+{\sum }_j{D}_j{\mu }^j/j!$. The total quality factor ($Q_{\mathrm{tot}}$) and extinction ratio (ER) are given by $$Q_{\mathrm{tot}}=\frac{\pi n_{g}L\sqrt{ra}}{{\lambda }_{\mathrm{res}}(1-ra)},$$(1)$$\mathrm{ER}=10\lg \frac{{(r-a)}^2{(1+ra)}^2}{{(r+a)}^2{(1-ra)}^2}.$$(2)

Based on the aforementioned equations^[39,40], the intrinsic quality factors of Cavity 1 and Cavity 2 are determined to be about $4.1\times {10}^6$ and $4.8\times {10}^6$, respectively. COMSOL simulations are employed to estimate the effective mode area of the waveguide, which is found to be $1.26{\mathrm{\mu m}}^2$. Consequently, the parametric oscillation^[41–44] thresholds of the two microcavities are calculated to be about 2.66 mW for Cavity 1 and 2.41 mW for Cavity 2, respectively. The measured fiber-chip-fiber insertion losses are 5.375 dB/facet for Cavity 1 and 4.880 dB/facet for Cavity 2, including propagation losses in the on-chip waveguides. The pump power for both cavities is amplified to approximately 23 dBm. The on-chip power of Cavity 1 is approximately 17 dBm, while the on-chip power of Cavity 2 is approximately 16.5 dBm. With the fine-detuning of the main laser’s frequency, we can access the soliton platform at a relatively slower rate. Then, a smooth single-soliton state can be reached.

To achieve high visibility in independent HOM interference for two independent DKS combs, it is necessary to eliminate the frequency differences between their comb lines. In order to simplify the experimental setup of the detection side, we put the frequency compensation part in the light source generation part. The frequencies of the comb lines can be expressed as $f_{\mu }=f_p\pm \mu \times \mathrm{FSR}$, where $\mu$ is the relative mode number with respect to the pump and $f_p$ is the frequency of the pump. Due to the thermo-optical effect, electrically driving the integrated heater changes the refractive index of the waveguide, thereby adjusting the spectral positions of the cavity resonances. Similarly, an optical signal spectrum containing modulation frequency information is generated through an electro-optical phase modulation process. Considering that the combination of an SSB modulator and a micro-heater is used for fine adjustment of comb-line frequencies, the frequency difference $\mathrm{\Delta }{f}_{\mu }$ between different combs can be expressed as $$\mathrm{\Delta }{f}_{\mu }=(f_{p_1}-f_{p_2})+\mu \times \mathrm{\Delta }\mathrm{FSR}+f_{\mathrm{SSB}}+f_{\text{heater}},$$(3)where $\mathrm{\Delta }\mathrm{FSR}$ is the FSR difference with different cavities, $f_{p_1}(f_{p_2})$ is the frequency of the pump of comb1 (comb2), $f_{\mathrm{SSB}}$ is the microwave signal frequency applied to the SSB modulator, and $f_{\text{heater}}$ is the frequency shift component by the micro-heater.

Once the robust soliton state of the two devices has been obtained, the crucial challenge is to control the pump laser in such a way that the same soliton states of the two microrings are accessed simultaneously. The slight difference in cavity length between the two microrings results in a difference in FSR, with ${\mathrm{FSR}}_2=100.54\mathrm{GHz}$ being slightly larger than ${\mathrm{FSR}}_1=100.41\mathrm{GHz}$. This naturally leads to a separation of the natural frequencies between the two frequency combs. To align the selected signal cavity mode (from CH38 to CH44), a voltage of approximately 7.85 V is applied to the integrated micro-heater on Cavity 2, utilizing the thermo-optical effect to induce a red shift in the entire Cavity 2 spectrum. The adjustment accuracy is 0.01 V, and the response is 2.26 pm/mW, with a maximum theoretical adjustment range of approximately 50 GHz.

Additionally, an SSB modulator is loaded on one of the optical paths of the auxiliary pump, allowing the simultaneous access of soliton platforms of two cavities. Given the employment of two independent main pump sources, it is imperative to consider the initial pump frequency differences for the purpose of compensation. Conversely, the relative frequency difference of the main pump position can be utilized for fine-tuning the comb lines, as Fig. 2(d) shows that the tuning length is allowed to exceed 30 MHz while maintaining the soliton states. The system’s stability has been demonstrated to exceed 8 h under these conditions (as shown in Fig. S5 in the Supplementary Information).

The DKS comb is filtered through cascaded 32-channel AWG filters with a 100 GHz bandwidth, resulting in a single-frequency light with an SNR exceeding 50 dB [as shown in Fig. S6(f) in the Supplementary Information]. The single-frequency comb lines are transmitted to the detection setup in another laboratory (Lab 2) through a single-mode optical fiber cable of about 600 m. An intensity modulator is used to prepare the WCS pulses. A polarization controller adjusts the polarization of the signal light before it enters the intensity modulator. The continuous light is chopped to a pulse series by IMs, on which the electrical signal with a repetition rate of 250 MHz and a width of about 400 ps is loaded.

The light pulses are projected into the HOM interferometer via a combination of a fiber polarization beam splitter and a fiber polarization-preserving beam splitter, which maintains the polarization of the two photons. The output photons are detected by SNSPDs and a field-programmable gate array (FPGA)-based coincidence logic unit records and analyses the photon detection signals. The coincidence count probability $P_{\text{coin}}(\tau )$ is a function of the delay time $\tau$ between pulses of two users: $$P_{\text{coin}}(\tau )=\frac{1}{2}-\frac{1}{4}V{e}^{-\frac{{\tau }^2}{2{\sigma }^2}}\cos (\tau \mathrm{\Delta }\omega ),$$(4)where $V$ represents the fringe visibility of HOM interference, $\sigma$ is the full width at half-maximum of the wave packet, and $\mathrm{\Delta }\omega$ is the frequency difference of the two interference photons^[45]. As Fig. 3 shows, multichannel HOM interference has been demonstrated from CH38 to CH47. The spectra of two soliton states are recorded separately by a spectral analyzer. In order to keep the pump mode [as shown in the dotted boxes of Figs. 3(b) and 3(c)] always in the flat position of the filter bandwidth when adjusting the frequency within the range of an FSR, the 200 GHz WDM is used as the post-filter. After compensating for the frequencies of different pairs of combs, respectively, we performed a time delay scan from $-800$ to 800 ps with a step of 50 ps. The experimental results are shown in Fig. 3(c), where the visibilities of HOM interference are distributed from $43.1\%\pm 0.6\%$ to $46.7\%\pm 0.6\%$. To evaluate the stability, the HOM interference of each comb-teeth pair is measured five times.

In this work, we demonstrate the frequency interference between different independent DKS combs using high-precision frequency translation and on-chip thermo-optical tuning. We have measured HOM interference visibilities of 10 pairs of single comb lines. The average visibility ranges from 43.14% to 46.72%, demonstrating that the independent DKS optical combs exhibit good indistinguishability comparable to measurement results using single-frequency lasers. Without using any frequency locking system, the soliton system platform remained stable for 8 h with the free-running lasers. It is anticipated that a longer-term and more stable multi-frequency broadband light source will be obtained if the pump laser is locked to the ultra-stable cavity. The findings of our research provide the possibility of a scalable and integrated platform for the realization of multi-user quantum networks.