Introduction

Multi-user entanglement distribution and analysis at different locations are practical requirements for quantum networks and distributed quantum computation. The systems often involve numerous independent building blocks, such as beam splitters (BSs), modulators and delay lines [1, 2], which always need a large space and bear mechanical and thermal disturbances [3, 4]. Compared to free-space optics and fiber optics, photonic integrated circuits (PICs) are promising platforms to overcome these difficulties due to their small footprint, scalability, programmability, and stability [5,6,7,8,9]. PICs provide opportunities to demonstrate large-scale quantum information processing that contains numerous optical components with millimeter scale, that is, quantum photonic integrated circuits (QPICs) [10, 11]. For example, multidimensional quantum entanglement [12], quantum teleportation [13] and various quantum algorithms [14,15,16,17] have been demonstrated on QPICs.

In quantum networks, to enhance the transmission capacity, make full use of wideband entangled photons [18,19,20,21] and increase the number of users, dense wavelength-division multiplexing (DWDM) techniques are often used for quantum communication and play a key role in many quantum network architectures [1, 22, 23]. Besides, compared to polarization and frequency entanglement, entanglement with time basis is insensitive to polarization and frequency dispersion in fiber transmission and can be maintained in fiber networks, and thus is widely used. For example, combining unbalanced Mach-Zehnder interferometers (UMZIs) with DWDM components, energy-time entanglement states are used for long-distance quantum entanglement distribution among multiple users [24,25,26]. To improve the compactness and practicability of the system, key components need to be integrated monolithically. In fact, we have seen many attempts in recent years. For example, UMZIs are integrated on the silicon nitride (SiN) platform to generate time bins and analyze entanglement [27, 28]. As a main choice for integrated DWDM systems [29], arrayed waveguide gratings (AWGs) have been integrated on silica [30, 31], silicon-on-insulator (SOI) [32,33,34], SiN [35], thin-film lithium niobate on insulator (LNOI) [36] and polymer platforms [37]. However, these works are subject to limited scale, and in particular, the two most critical components—DWDMs and UMZIs have not been completely integrated on one single chip.

In this work, we realize the integration of a 32-channel high-performance AWG and 32 UMZIs on a single chip based on a high-index doped silica (HIDS) platform for large-scale quantum networks. Furthermore, we achieve the multi-wavelength energy-time entanglement distribution among three chips. As shown in Fig. 1, one fiber-packaged silicon nanowire works as the sender to generate wideband quantum photon pairs, and the other two receivers are integrated on the HIDS platform for the preparation and analysis of the energy-time entanglement. On the receiver chips, multiple wavelength channels support simultaneous operations by different users. Even if the chips are separated with 1-kilomiter-long fibers, the high quantum interference visibility is achieved and proves the effectiveness of the multi-chip system. The system will play an important role in dense quantum communication and building up practical quantum networks.

Fig. 1
figure 1

Schematic diagram of multi-chip interconnection for energy-time entanglement distribution. The silicon-on-insulator chip is the sender and generates correlated wideband photon pairs via the spontaneous four-wave mixing process. The photons are divided and sent to two receivers of the quantum network. At the receiver terminal, photons are subdivided into different wavelength channels by the AWG. Entanglement preparation and analysis are carried out by the on-chip UMZIs. The energy-time entangled photons are detected by single photon detectors. AWG: arrayed waveguide grating; UMZI: unbalanced Mach-Zander interferometer

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Results

Details of the photonic chips

The quantum photon-pair source serves as the sender. It includes one SOI helical waveguide with a cross section of 220 nm × 500 nm. Wideband correlated photons are generated via the spontaneous four-wave mixing (SFWM) process in the waveguide [38]. The HIDS chips serve as the receivers. The 1 × 32 AWG, 32 balanced MZIs and 32 UMZIs are integrated on a single chip (shown in Fig. 2(a)). The waveguide has a cross-section of 2 × 2 μm to support single mode propagation. The waveguide transmission loss is very low, ~ 0.05 dB/cm, which is ideal for on-chip long-time delay. Two arms of the UMZI have a relative time delay of 400 ps (unbalanced length is ~ 7.38 cm, which introduce an extra loss of ~ 0.37 dB), which is used to distinguish the photon coincidence counting peaks. A balanced MZI is employed in the short arm of the UMZI for energy compensation through modulation of the on-chip platinum micro-heater (not shown in Fig. 1(a)). The phase differences of the two arms of UMZIs are tuned using micro-heaters covering the delay spiral waveguides. The size of the on-chip integrated 1 × 32 AWG is 6.2 mm × 8.0 mm (Fig. 2(b)). The 3-dB passband width of the AWG channel is approximately 0.3 nm, and the insert loss variation is less than 4 dB for all channels. The crosstalk among all channels is less than − 30 dB. The wavelength and channel spacing of the AWG meet the standard international telecommunications union (ITU) grids. All the input and output waveguides are arranged in a column with a pitch of 127 μm coupled by a 128-channel fiber array. The coupling loss is less than 1.5 dB/facet. We select 17 channels, and their transmission spectra are shown in Fig. 2(d).

Fig. 2
figure 2

Characterization of the samples. a A CCD photograph of the energy-time entanglement preparation chip, composed of a 32-channel AWG, 32 balanced MZIs and 32 UMZIs, 64 on-chip heaters, coupled with a 128-channel fiber array. b-c Microscope images of the AWG and UMZI. d Transmission of the 17 selected channels of the AWG, centered at C50 of international telecommunications union (ITU) grids

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Entanglement distribution of one sender and one receiver

Firstly, we distribute the multi-wavelength correlated photons to one receiver chip. As shown in Fig. 3(a), a continuous-wave laser (TSL-550, Santec) centered at 1537.40 nm (center of the C50 channel of ITU grids) is used as the pump (23 mW off chip) to generate photon pairs through the SFWM process in an SOI waveguide on Chip I. We use one PC before chip I to vary the polarization of the pump to guarantee maximum photon-pair generation. A prefilter of 100 GHz is utilized to eliminate noise, mainly the broadband background fluorescence of the amplified spontaneous emission effect in the pump laser. A post filter of 200 GHz is used to reject the residual pump and protect the single photon detectors. Both filters exceed 100 dB isolation. After narrowing the bandwidth with one bandpass filter, the generated photon pairs are injected into Chip II, which is composed of an AWG and UMZIs. We use this chip for the energy-time entanglement preparation and analysis. The polarization of photons injected into Chip II is also fixed by another PC (not shown) to ensure TE0 mode excitation.

Fig. 3
figure 3

Experimental setup and results for multi-channel entanglement distribution of one sender and one receiver. a Experimental setup. A silicon-on-insulator waveguide on Chip I serves as a quantum source. Chip II is the energy-time entanglement preparation and analysis chip. b-c Typical histograms of the interference peaks for CH11&CH7 of the AWG. The time resolution of the histograms is 40 ps. d The raw coincidence of the central peak for i1-s1 changes with phase. The black dots are measured coincidences. The gray curve is obtained by fitting the measured results using the sine function. The error bar comes from the Poisson statistical distribution. Red and blue dots refer to single channel counts of idler and signal photons, respectively. PC: polarization controller; VOA: variable optical attenuator; EDFA: erbium-doped fiber amplifier

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The AWG serves as a critical DWDM component. It has 32 output ports, as shown in Fig. 2(b). We select 17 of them to demonstrate the entanglement distribution experiment (transmission spectra shown in Fig. 1(d)) and label them as CH1 to CH17 by wavelength from long to short. Their functionalities and the correspondence with standard DWDM channels are given in Table 1. The output photon pairs are detected by superconducting nanowire single-photon detectors (SNSPDs, Scontel) with time jitter 45 ps. The generated electric signals are imported into the time-correlated single photon counting (TCSPC) system for the correlation analysis.

Table 1 Definition and quantum interference visibilities of the AWG channel pairs. “s” and “i” represent “signal” and “idler” photons, respectively. It should be noted that the central three channels (CH8, CH9 and CH10) of the AWG are in the range of the post filter (gray zone in Chip II in Fig. 3(a)). Thus, their visibilities are absent
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In the experiment, the spiral on Chip II provides a time delay (ΔT) of 400 ps, which meets the condition for energy-time entanglement generation. That is, τ2 ≪ ΔT ≪ τ1, where τ2 is the coherence time of the single photons (~ 25 ps, which is estimated by the reciprocal of the photon bandwidth) and τ1 is the coherence time of the continuous pump laser [39]. The photonic state after the AWG and UMZIs can be described as \(\frac{\left({e}^{i{\varphi}_i}{\left|L\right\rangle}_i+{\left|S\right\rangle}_i\right)}{\sqrt{2}}\) and \(\frac{\left({e}^{i{\varphi}_s}{\left|L\right\rangle}_s+{\left|S\right\rangle}_s\right)}{\sqrt{2}}\), where φi and φs are the phase differences introduced by UMZIs for the idler and signal photons, and “L” and “S” represent the “Long” and “Short” time bins, respectively. The two-photon state is the direct product of single-photon states, which has the form of

$$\frac{1}{\sqrt{2}}\left({e}^{i{\varphi}_i}{\left|L\right\rangle}_i+{\left|S\right\rangle}_i\right)\otimes \frac{1}{\sqrt{2}}\left({e}^{i{\varphi}_s}{\left|L\right\rangle}_s+{\left|S\right\rangle}_s\right)=\frac{1}{2}\left({e}^{i\left({\varphi}_i+{\varphi}_s\right)}{\left|L\right\rangle}_i{\left|L\right\rangle}_s+{e}^{i{\varphi}_i}{\left|L\right\rangle}_i{\left|S\right\rangle}_s+{e}^{i{\varphi}_s}{\left|S\right\rangle}_i{\left|L\right\rangle}_s+{\left|S\right\rangle}_i{\left|S\right\rangle}_s\right),$$

and will be recognized by the TCSPC system as three coincidence peaks separated by “ΔT” (see Fig. 3(b-c)). The central peak (a time delay of 0) indicates the energy-time entanglement state, which has the form of

$$\left|\varphi \right\rangle =\frac{1}{\sqrt{2}}\left({e}^{i\left({\varphi}_i+{\varphi}_s\right)}{\left|L\right\rangle}_i{\left|L\right\rangle}_s+{\left|S\right\rangle}_i{\left|S\right\rangle}_s\right).$$

The central peak coincidence C is proportional to (1 + V cos(φi + φs)), where V is the visibility of the coincidence curve. By tuning the phases φi + φs with on-chip heaters, we test every correlated channel pair and list their quantum interference visibilities in Table 1. All raw visibilities are over 90%, which proves that the integrated circuits have high quality and are ready for further quantum information applications. The typical coincidence curve of CH11&CH7 (C52&C48 of ITU) and their single channel counts as a function of phase on the long arm of UMZI are shown in Fig. 3(d). Coincidence curves for other channels can be found in the Supplementary Materials.

Entanglement distribution of one sender and two receivers

The results of the former experiment prove that our chips work well in generating and analyzing energy-time entanglement. Furthermore, we verify the feasibility of the chips for entangled distribution among three chips. In this part, we add another receiver chip (see Fig. 4 (a)). The photons generated by the SOI waveguide are divided by one BS and then sent to two receiver chips, namely, Chip II-a and Chip II-b for energy-time entanglement analysis. Two 1-km-long standard SMF-28e fibers connect the BS with the following two chips. We selected three equally spaced channel pairs and measured their coincidence versus phase. The quantum interference visibilities are listed in Table 2. All the raw visibilities are over 85%.

Fig. 4
figure 4

Experimental setup of multi-channel entanglement distribution of one sender and two receivers. a Experimental setup. A silicon-on-insulator waveguide on Chip I serves as a quantum source. Chip II-a and Chip II-b are energy-time entanglement preparation and analysis chips, which serve as the receivers. Standard single mode fibers with one-kilometer length connect the chips b The raw coincidence of the central peak for CH11&CH7 versus phase. The black dots are measured coincidences. The gray curve is obtained by fitting the measured results using the sine function. The error bar comes from the Poisson statistical distribution. Red and blue dots refer to single channel counts of idler and signal photons, respectively

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Table 2 Definition and quantum interference visibilities of the AWG channel pairs in the multi-chip entanglement distribution
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Discussion

In the experiment, the arm length difference of the UMZIs is 400 ps, which is mainly limited by the detectors’ time jitter and coherence time of the single photons. Using a temporally narrowband light source and smaller time jitter detectors, we are able to decrease the arm length difference, which facilitates further construction of high-dimensional energy-time entanglement on the single chip. Due to the ultralow transmission loss of the HIDS waveguide, long time delay UMZIs can be easily achieved. On the basis of our structure, a multi-wavelength high-dimensional energy-time entanglement distribution can be demonstrated by the cascade of UMZIs, thereby further increasing the system capacity. With another on-chip UMZI to modulate the pulsed pump laser, our scheme can be easily extended to another commonly used scheme, the time-bin entanglement distribution [40]. Because multiple-wavelength channels of the receiver chips support simultaneous operations by different users and more nodes can be constructed with more similar integrated chips, our work advances the quantum technologies for large-scale and complex quantum networks.

Conclusions

This work first integrates DWDM components with UMZIs monolithically and demonstrates multi-chip entanglement distribution with high interference visibilities. Benefiting from the low loss, low optical nonlinearity and high integration density of the HIDS platform, this work is promising for extending to high-dimensional energy-time and time-bin entanglement distributions among multiple users. With many other integrated structures, more complex and larger quantum networks will be built.

Methods

Thermal control is critical to the experiment. The resistance of heaters on the short balance MZIs is ~ 170 Ω, which requires a current of ~ 50 mA to adjust a 2π phase. The heaters on the spiral waveguide of UMZIs have resistance of ~ 1.5 kΩ, and a current supply of ~ 14 mA is enough to finish a coincidence curve measurement. In our experiment, a custom-made high-power current source is used. To stabilize the operation temperature during the experiment, the integrated chip is mounted on a thermoelectric cooler (TEC), which is driven using a TEC controller (TED200C, Thorlabs). Conductive silver glue is used to fill the contact surfaces (see Supplementary Materials). The temperature coefficient of the AWG central wavelength is ~ 18 pm/°C, which can be utilized to align the central wavelength of the AWGs with the standard of ITU grids and ensure that the system works properly.