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Abstract
Cryogenic integrated nonlinear photonics can provide fundamental building blocks for scalable photonic quantum computing and optical interfacing among different platforms. Here, we investigate the spontaneous four-wave mixing effect in an integrated silicon waveguide with cryogenic operating conditions (4 K) and employ the system to generate the entangled photon-pair source, one of the key elements of photonic quantum information applications. We experimentally prove that even at cryogenic temperatures, the four-wave mixing effect in silicon waveguides is still an effective method to generate quantum photonic sources. The cryogenic photon-pair source is verified over multiple frequency channels within a bandwidth of ${\sim}2\;{\rm{THz}}$. Furthermore, the source is used to generate high-quality frequency-multiplexed energy–time entangled states. Our results will advance the development of cryogenic nonlinear photonics and scalable integrated photonics for quantum information processing.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
Photonic integrated circuits (PICs) have developed into a compelling platform to providing fundamental building blocks for a wide range of quantum information applications [1]. By using optical waveguides to guide and route photons, this technology provides phase-stable circuitry with millimeter-scale footprints for different quantum core functionalities, such as nonclassical photonic quantum sources [2–5], programmable photonic quantum processors [6–11], and single-photon detectors [12–14]. Furthermore, because photons can be transmitted over a long distance via optical fiber and are thus essential for constructing quantum networks [15], quantum PICs (QPICs) are becoming a possible candidate to interface different quantum systems with hybrid integrated techniques [16].
Until now, most investigations on QPICs have focused on operation at ambient temperatures; however, many quantum components, such as superconducting nanowire single-photon detectors (SNSPDs) [12,13], as well as semiconducting and superconducting quantum computing systems [17,18], have to operate under cryogenic conditions. For scalable photonic quantum computing and interfacing among different quantum systems, quantum technologies must be mutually compatible. Therefore, QPICs that are optimized to operate at room temperature, in particular, those involving nonlinear processes, should be extended to cryogenic environments [19].
The four-wave mixing effect in integrated waveguides is widely used in a variety of nonlinear processes and has great prospects in all-optical signal processing for classical and quantum applications. For example, combined with the four-wave mixing effect, silicon photonics provides a versatile test bed for quantum photonics and plays an important role in scalable photonic quantum information applications [20]. This nonlinear effect can generate new frequencies and effectively realize different functions in various configurations, such as wavelength conversion and parametric amplification [21–23], heralded single photons [24–26], two-photon and multi-photon entangled states [27–32], and squeezed states [5,33,34]. Demonstrating this capability under cryogenic operating conditions will undoubtedly expand the application scope of PICs.
In this paper, we investigate the spontaneous four-wave mixing (SFWM) effect in an integrated silicon waveguide under cryogenic operation conditions (4 K). We experimentally prove that SFWM in silicon waveguides is still an effective method to generate quantum photonic sources at cryogenic temperatures. Cryogenic photon pairs were generated and experimentally verified with a bandwidth of ${\sim}2\;{\rm{THz}}$, and noise generated in the photon-pair source preparation was carefully analyzed. Furthermore, by feeding correlated photon pairs into a common unbalanced Michelson interferometer (UMI, 1.6 ns time difference), frequency-multiplexed energy–time entangled states were generated and analyzed. Near-unity raw interference visibilities were observed for multi-channel pairs, indicating the high quality of the cryogenic source. Our results represent an important part of cryogenic nonlinear photonics and will be further used in integrated scalable quantum information applications.
Fig. 1. Experimental setup. The integrated silicon waveguide and fiber array are placed in the closed-cycle cryostat. The fiber array and two on-chip end couplers are used for coupling the input pump and output signal–idler photons. Inset: frequency-multiplexed photon-pair generation using the silicon waveguide. CW Laser, continuous-wave laser; PC, polarization controller; DWDM, dense-wave-division multiplexer; SNSPD, superconducting nanowire single-photon detector.
2. EXPERIMENTAL SETUP AND RESULTS
A. Experimental Setup
In the experiment, a continuous-wave (CW) laser (Santec, central wavelength 1550.12 nm) was used as the pump source. As shown in Fig. 1, the pump first passed through two cascaded 100 GHz bandwidth fiber pre-filters (filter 1, 100 dB extinction ratio) to remove the background noise. Then, it was coupled into the silicon device by a single-mode fiber array in a closed-cycle cryostat (Montana Instruments). A fiber polarization controller was placed between the filter and cryostat to adjust the polarization of the pump in the silicon waveguide, which was kept in ${{\rm{TE}}_0}$ mode in the experiment. The silicon waveguide is 1.2 cm long with a cross section of $500 \times 220\;{\rm{n}}{{\rm{m}}^2}$, which satisfies the near-zero phase matching condition for SFWM. The generated signal–idler photons were input into a 40-channel dense-wave-division multiplexer (DWDM) to separate the signal and idler photons. Each DWDM frequency channel has a 100 GHz bandwidth, such that we can select multiplexed frequency combinations for photon pairs with a frequency detuning of ${\sim}2\;{\rm{THz}}$ from the central pump frequency. The central wavelength of each DWDM channel and correspondence between the index of signal–idler channels (${\pm} 1 {-} {\pm} 19$) and international telecommunication union grids (C15–C53) are given in Table S1. Before the DWDM, we used two cascaded off-chip 200 GHz bandwidth fiber post-filters (filter 2, 100 dB extinction ratio) to block the pump light. The generated photon pairs were detected by two SNSPDs, which have dark count rates of approximately 100 Hz. Finally, the acquired electrical signals were collected and analyzed through the time-correlated single-photon counting system.
B. Photon-Pair Source Characterization
By adjusting the temperature of the cryostat, we first recorded photon-pair production at 4 K and 294 K (i.e., room temperature) with 2 mW pump power (off-chip), and the experimental results are shown in Fig. 2. Note that the 294 K results are only for comparative analysis. With the pump wavelength as the center, the frequencies of the correlated photon pairs were equally separated. The DWDM system gives 38-channel single-photon counts (${N_s}$ and ${N_i}$, where $s$ represents the signal and ${i}$ represents the idler) and 19 photon-pair coincidence values (${C_{{\exp}}}$). By comparing the emission spectra at different temperatures [Figs. 2(a) and 2(d)], we found that the emission at 4 K was reduced, especially for channels close to the pump. Specifically, the photon flux decreased by 65% on average at frequencies lower than that of the pump and 68% on average at frequencies higher than that of the pump. As we know, this emission reduction has two main causes: one is SFWM reduction under cryogenic conditions, which is due to the attenuation of optical Kerr nonlinearity in the silicon waveguides [35], and the other is the noise suppression caused by cryogenic cooling [36]. The coincidence values for different channels are shown in Figs. 2(b) and 2(e). We can see that even at cryogenic temperatures, two-photon coincidence covers all channels, and SFWM in silicon waveguides is still an efficient method to prepare parametric quantum photonic sources. The brightness reduction is due to the attenuation of the optical Kerr nonlinearity in the silicon waveguides. Owing to the difference in efficiency with signal–idler channels in post-filtering and DWDM systems (see Table S1), we have normalized both the single channel and coincidence results here. The fluctuation in the emission spectra and coincidence results of different channels stems from the discrepancy in channel bandwidth, unfiltered laser noise, and fluctuation in coupling efficiency during the test. On average, the detected source brightness at 4 K was 41% lower than that at room temperature, which corresponds to a reduction in the Kerr nonlinear coefficient of approximately 23%. This value is consistent with the results in Ref. [35], which discussed the effect of temperature on optical nonlinear parameters in detail. Compared to coincidence counts, single-photon counts drop even more at 4 K, which is mainly caused by noise suppression resulting from cryogenic cooling. The ratio of the net coincidence value ${C_{{\rm{net}}}}$ and accident coincidence event $A$ (CAR) is one key parameter for characterizing photon-pair sources. Using the formula ${\rm{CAR}} = {C_{{\rm{net}}}}/A$, we calculated the CAR values of different signal–idler channels at 4 and 294 K. In the formula, ${C_{{\rm{net}}}} = {C_{{\exp}}} - A$ and $A = {N_s}{N_i}{t_{{\rm{win}}}}{t_{{\rm{int}}}}$, where ${t_{{\rm{int}}}}$ is the coincidence integral time and ${t_{{\rm{win}}}}$ is the coincidence window. The results are shown in Figs. 2(c) and 2(f), respectively, and the CAR values improved at 4 K compared to those at 294 K. It is particularly noteworthy that at the channels close to the pump frequency, such as signal–idler channels ${\pm} 2$, the CAR exceeded 500:1, whereas in the room temperature case, it was less than 23:1. This CAR improvement enables more frequency channels to be used for further quantum information applications. In addition, because of noise suppression, a higher heralding efficiency can be achieved with this cryogenic photon-pair source (see Supplement 1). To explain the pattern of CAR in more detail, we further split the single-photon count into SFWM signals and noise. The CAR of the photon-pair source can be described as
Fig. 2. Frequency-multiplexed photon-pair sources generated at cryogenic and room temperatures with a silicon photonics chip. (a) Continuous emission spectra at 4 K from the 40-channel DWDM system. The frequencies of the correlated photon pairs are equally separated from the central pump frequency. (b) Coincidence measurements in 20 s intervals of the photon pairs in different frequency channels at 4 K. (c) CAR values in different frequency channels at 4 K and the corresponding fitted curve. (d) Continuous emission spectra at 294 K. (e) Coincidence measurements of the photon pairs at 294 K. (f) CAR values in different frequency channels at 294 K and the corresponding fitted curve. All data are averages of two consecutive measurements, from which error bars of CAR values are given.
We take one common channel, C43, as an example and estimate the proportion of noise generated in the silicon waveguide and fiber to the detected single-photon count at this channel. At room temperature, noise in the fiber and silicon waveguide accounts for 12% and 30%, respectively. At 4 K, the noise in the silicon waveguide was negligible, and the noise in the fiber accounts for 25% of the single-photon count. Because the fluorescence noise in the fiber is proportional to the fiber length, we can reduce the length of the fiber between filters to mitigate the influence of noise in the fiber.
By combining SFWM and SpRS, we fitted the CAR data. The CAR fitted curves for different temperatures are also given in Figs. 2(c) and 2(f). Considering that the dark count of single-photon detectors is much lower than the detected single-photon count, we neglected them in fitting for simplicity. The fitted source brightness at different temperatures is $G({{4}}\;{\rm{K}})\;{ = }\;{{107}}\;{\rm{kHz}}$ and $G({{294}}\;{\rm{K}})\;{ = }\;{{1003}}\;{\rm{kHz}}$, which are close to the theoretical estimation (see Supplement 1).
To better understand the properties of photonic sources at cryogenic temperatures, we chose correlated frequency channels ${\pm} 9$ as an example and recorded the coincidence and CAR results with 2 mW pump and temperatures ranging from 4 to 294 K. The experimental results are shown in Figs. 3(a) and 3(b), and we can see that as the temperature rises, the brightness of the photon-pair source increases while the CAR decreases. The brightness of the source is proportional to the square of the Kerr nonlinear parameter, and the data can be fitted based on the empirical formula in Ref. [35]. It has the form of
Fig. 3. Temperature and pump power dependence of the photon-pair source with correlated frequency channels ${\pm} 9$. (a) Temperature dependence of the source brightness and the fitted curve. (b) Temperature dependence of CAR and the fitted curve. (c) Two-photon coincidence results as a function of the input pump power at 4 and 294 K. The data were obtained with different integration times and normalized according to the integration time. (d) CAR values as a function of the input pump power at 4 and 294 K.
In many cases, such as multi-photon applications, the photonic sources with the pulsed laser pump are always used, which show lower noise than that with the CW laser pump. With 160 µW picosecond pulsed laser pump power [2], we also recorded the coincidence and CAR results at different temperatures. The results are shown in Fig. 4, and coincidence values show a similar pattern as in the CW laser pump. Although the improvement is not as pronounced as in the case of the CW pump, the CAR value is also improved at lower temperatures.
Fig. 4. Temperature dependence of the photon-pair source’s (a) brightness and (b) CAR with pulsed laser pump.
Fig. 5. Energy–time entanglement interference measurements. (a) Experimental setup for entanglement generation and detection. (b) Coincidence results as a function of the total UMI phase for photon-pair source with frequency channels ${\pm} 9$. (c) Interference visibility for six correlated channels. UMI, unbalanced Michelson interferometer; DWDM, dense-wave-division multiplexer.
C. Entanglement Generation and Verification
This cryogenic integrated photon-pair source has many applications, one of which is to generate quantum entangled states, which lies at the heart of quantum information studies. Here, we used one common UMI to generate energy–time entanglement, which is widely used for quantum information processing, such as quantum cryptography [42] and Bell-type tests [43]. The UMI consists of one 50/50 beam splitter, two Faraday mirrors, and the connected optical fiber. In the experiment, the signal and idler photons generated by the silicon nanowire at 4 K were first input into the UMI and then separated by the DWDM for further detection and analysis [Fig. 5(a)]. By post-selection of the central peak of the coincidences with a 0.4 ns time window, we obtained the energy–time entangled state in the form of
3. DISCUSSION AND CONCLUSION
Our work experimentally confirms that even under cryogenic conditions, SFWM in silicon waveguides is still an efficient method for generating quantum photonic sources. Cryogenic cooling suppresses noise, and a high-quality quantum photonic source is achieved. Combined with cryogenic integrated photonic modulators [45,46], a variety of photonic quantum applications can be performed using QPICs under cryogenic operation conditions. In particular, SNSPDs with excellent performance also operate at similar temperatures. Integrated photonic devices that contain all core functions, such as photonic source generation, quantum state modulation, and single-photon detection, will greatly reduce chip-in and chip-out losses, thus promoting photonic quantum applications in daily life. For fully integrated operation, pump filtering at cryogenic temperatures is also very important, and verifying its functions will be the next step. Beyond the quantum photon-pair source, our work will promote other cryogenic nonlinear applications such as all-optical modulation, wavelength conversion, and parametric amplification with silicon photonic circuits.
In conclusion, we demonstrate quantum photon-pair source preparation with integrated silicon photonic circuits under cryogenic conditions. It has been proven that SFWM in silicon waveguides is still an efficient method for generating quantum photonic sources at this low temperature. Photon pairs are experimentally verified with a bandwidth of ${\sim}2\;{\rm{THz}}$, and frequency-multiplexed energy–time entangled states are generated. The observed near-unity interference visibility indicates that this cryogenic multichannel entangled photonic source has high quality and is ready for further quantum information applications. Our work is an important part of cryogenic nonlinear photonics and will be further used for scalable quantum information applications.
Funding
Innovation Program for Quantum Science and Technology (2021ZD0301500, 2021ZD0303200); National Natural Science Foundation of China (12004373, 62061160487, 62275240); Key Research and Development Program of Anhui Province (2022b1302007); China Postdoctoral Science Foundation (2021T140647); Fundamental Research Funds for the Central Universities.
Acknowledgment
We thank Chen-Wei Chen for useful suggestions on revising the language of this article. This work was partially carried out at the USTC Center for Micro and Nanoscale Research and Fabrication.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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