Quantum information has the potential to bring revolutionary performance for computation, communication, and metrology applications in terms of speed,1,2 security,3
Advanced Photonics Nexus, Volume. 2, Issue 1, 016003(2023)
Deterministic N-photon state generation using lithium niobate on insulator device Article Video , On the Cover
The large-photon-number quantum state is a fundamental but nonresolved request for practical quantum information applications. We propose an N-photon state generation scheme that is feasible and scalable, using lithium niobate on insulator circuits. Such a scheme is based on the integration of a common building block called photon-number doubling unit (PDU) for deterministic single-photon parametric downconversion and upconversion. The PDU relies on a 107-optical-quality-factor resonator and mW-level on-chip power, which is within the current fabrication and experimental limits. N-photon state generation schemes, with cluster and Greenberger–Horne–Zeilinger state as examples, are shown for different quantum tasks.
1 Introduction
Quantum information has the potential to bring revolutionary performance for computation, communication, and metrology applications in terms of speed,1,2 security,3
On the other hand, photons are known for their weak interaction, where long coherence time can be achieved even at room temperature, which makes them suitable for “flying qubits” applications.17
Here we propose the first feasible scheme to deterministically generate an -photon state, considering the practical material capability. Such a scheme is based on an ensemble of basic units called photon-number doubling units (PDUs) that is used to realize photon number doubling and keep their spectrum unchanged at the same time. This unit is capable of deterministic parametric downconversion (DPDC) and deterministic parametric upconversion (DPUC). Taking advantage of the strong nonlinear interaction in lithium niobate on insulator (LNOI) circuits,29
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2 Scheme
In general, an -photon state can be generated by cascading two-photon generation processes, either via or nonlinearity.28 Here we choose the LNOI circuit to realize parametric downconversion (PDC) with unitary efficiency because of its high nonlinearity, 34,37,38 low propagation loss,39 and strong mode confinement.40 As shown in Fig. 1, the photon number can be scaled using a standard PDU. Photon number doubling can be achieved using DPDC, while it is also necessary to include a DPUC unit for frequency upconversion so that the wavelengths remain unchanged after each step of the PDU. The DPUC resolves the problem of the increasing photon wavelengths as the DPDC processes cascade, and the long wavelength exceeds the transparency window of materials eventually and raises challenges for single-photon detector technology. With the photon wavelength unchanged, we can use a standard design as a fundamental building block for all PDUs at different stages, which is important for scalable photonic integration.
Figure 1.Scheme for deterministic
The practical layout of each PDU can be illustrated in Fig. 2(a), in the form of LNOI circuits. We choose a quasiphase-matched high- microring resonator for the DPDC process. The reason is twofold. First, the microring resonator can greatly enhance the photon interaction in a small footprint, and our modeling and calculation shows that DPDC can be achieved, considering the ultrahigh nonlinearity in the LNOI. Second, the cavity enhancement can keep the single-photon spectra unbroadened with a proper resonator design, while in the case of a nonresonant parametric downconversion process, the photon bandwidth is determined only by the phase-matching bandwidth, which is normally on the order of hundreds of GHz.41,42 It is a fundamental challenge to manage the phase matching over such increasingly broadened photon bandwidths.
Figure 2.The example for the PDU and
In our layout, the DPDC is nondegenerate in frequency so that the signal and idler photons can be separated by the on-chip wavelength division multiplexing (WDM1) device. Such WDM devices have been reported in the LNOI using different designs including a Mach–Zehnder interferometer43 and a multimode interferometer.44 Then the parametric photons enter centimeter-long periodically poled LNOI (PPLNOI) spiral waveguides for the DPUC. With a LNOI waveguide of such length, our calculation shows that unitary upconversion efficiency can be achieved via a sum-frequency generation (SFG) process with a single-mode SFG laser and only mW-level continue-wave power. Different SFG laser wavelengths are chosen for the signal and idler photons so that they are up-converted to the same wavelength as the pump before entering the PDUs in the next stage. The residue SFG laser is rejected using WDM2/WDM3 from the up-converted single/idler photons, respectively, and may be reused to up-convert the single/idler photons PDUs in the next stage. Only two SFG laser wavelengths are required over the whole -photon generation chip that greatly simplify the setup. An -photon state generation can be achieved by the integration of these PDUs, and the example in Fig. 2(b) shows the Fock state generation by direct cascading PDUs.
3 Results and Discussions
3.1 Model of Deterministic Parametric Downconversion
We model the DPDC process using the cavity-enhanced dual potential operators for quantization of the electromagnetic field,45
It differs from the normal SPDC model with all the interacting light field quantized including the pump using , where , , and represent the pump, signal, and idler, respectively. is the corresponding operator of the vector field , which is defined by the electric displacement field , with .45
To have unbroadened spectra for -photon state generation, single-longitude-mode (SLM) oscillation must be achieved in this cavity-enhanced case, which requires the difference of the free spectrum range of the signal and idler light to be larger than the linewidth of the cavity resonances.48,49 Such a condition is easily satisfied in the high- case, where such a high -factor is also necessary for the high efficiency as required by the DPDC on the other hand. At a certain resonator size and dispersion, the requirement of SLM oscillation can be derived as (see details in Sec. B in the Supplementary Material)
Figure 3.Calculation results of the PDC and PUC efficiency in the LNOI circuit. (a) The relation between the PDC efficiency
Under the SLM oscillation condition, it is reasonable to narrow the integration range for in Eq. (2) to around a single longitude mode , which is chosen to be here. In addition, , , and can be approximated as constants at center frequencies. Consequently, the dual potential can be rewritten as
To further simplify the Hamiltonian, we introduce the “normalized discrete Hilbert-space photon annihilation operator” 45 and get (see Sec. C in the Supplementary Material for details)
Taking the radius LNOI microring resonator as an example, we calculate the required value for DPDC (see Sec. E in the Supplementary Material for more details). Such a radius is chosen for a modeling with the LNOI microring on the buried oxide layer, and the bending loss induced limit is still over . Following Eq. (7), we first obtain by calculating the refractive indices , wave vectors , effective spatial overlap , and mode area for different wavelengths. Substituting into Eq. (9), we obtain the relation between and under different wavelengths, as shown in Fig. 3(a). For example, for the PDC process 646.91 nm → 1276.80 nm + 1311.29 nm, DPDC can be achieved with a relatively low of at 1311.29 nm, which is experimentally feasible considering the over for the LNOI resonator in experiments.34,40,54 We also calculate the required for DPDC under different microring radii , the results are shown in Fig. 3(b).
We assume a lossless model in the above discussion, and this assumption stands when the loss-induced is much higher than the required as discussed here. Considering the current material-absorption-limit of over ,55 the 42.2% total conversion efficiency is expected, which can be further reduced by the fabrication technique improvement (see Sec. H in the Supplementary Material for details).
3.2 Model of Deterministic Parametric Upconversion
We also model the DPUC process as the single-photon SFG with classical laser light. Here we take the DPUC process with SFG1 laser as an example, and the other DPUC process can be calculated using the same method. The SFG1 laser light can be considered as nondissipative, so that the Hamiltonian of the upconversion process can be written as56,57
Then we calculate the parametric upconversion efficiency under different SFG laser powers and waveguide lengths (see detail calculation in Sec. E in the Supplementary Material). To consist with the DPDC process, we choose the 1276.80 nm (single photon) + 1311.29 nm (SFG1 laser) → 646.91 nm and the 1276.80 nm (SFG2 laser) + 1311.29 nm (single photon) → 646.91 nm process. The calculation results are shown in Figs. 3(c) and 3(d), where the blue curve represents the condition for DPUC.
The DPUC has already been achieved in many platforms, such as reverse-proton-exchanged (RPE)58
3.3 Entanglement States Generation
In addition to the -photon Fock state, many other -qubit states, which are the key resource for practical quantum technology applications, can also be generated deterministically using PDUs. As examples shown in Fig. 4, we propose the on-chip design for -photon cluster states and GHZ states, which are the key for one-way quantum computation,62
Figure 4.Circuit design for generating different
4 Conclusions
We present a scheme for an arbitrary -photon state generation with an unlimited photon number in principle, where the -photon Fock state, GHZ state, and cluster state are taken as examples to demonstrate the detail design. Such scheme, utilizing the high-nonlinearity LNOI circuit, makes large-size quantum state generation experimentally feasible for the first time to our knowledge. The key component in the design is an ensemble of scalable standard basic units called PDUs. Based on our calculation, in the unit, DPDC and DPUC can be achieved with -factor microring resonators, 1-cm-long waveguides and 8-mW SFG powers in this unit, respectively. These numbers have been reported separately in the existing experimental papers on LNOI.36,69,70 This requirement can be further relaxed if the LNOI microring resonator is fabricated with a smaller radius in the air-cladding case,51,71,72 where the bending loss is maintained at a negligible level because of the increase in the the refractive index contrast between the lithium niobite waveguide and the cladding material. The strong field confinement of the LNOI also enables a small PDU footprint for the potential large-scale integration, paving the route to the large photon number generation on a single chip. The remaining challenges for the experimental demonstration are technical problems, which are not unrealistic in principle, including propagation loss reduction, resonance matching, and fabrication error control in the PDUs. We show that the strong single-photon interaction is possible in LNOI devices, and it is utilized for the -photon state generation but may not be limited for this application as discussed here. This strong single-photon interaction can also be used for photon manipulation to realize quantum gates, quantum storage, etc., to push forward the development of quantum computation,27 quantum communication,4,7,8,26 and the overall quantum information technology.
Huaying Liu is a postdoctoral research scientist at Nanjing University, School of Physics. She received her PhD degree at Nanjing University in 2021. Her research focuses on quantum optics and quantum information. She has demonstrated the first drone-based photon entanglement distribution, and optical-relayed photon entanglement distribution, which found the basis of the mobile quantum network. She has published over ten papers in high impact journals, including National Science Review and Physical Review Letters.
Minghao Shang is a PhD student at Nanjing University, School of Physics. He received his BS degree in physics from Harbin Institute of Technology. He joined Prof. Shining Zhu and Prof. Zhenda Xie’s Quantum Optics Group in 2019. His research interest is focused on quantum optics, integrated optical quantum technologies, and quantum information.
Yan-Xiao Gong obtained his PhD degree in optics from University of Science and Technology of China in 2009. In 2009, he joined Nanjing University as a postdoctoral research scientist. From 2011 to 2017, he worked in the Department of Physics at Southeast University. He is now a professor at the School of Physics of Nanjing University. He is currently working on nonlinear optics, quantum optics, and integrated optical quantum technologies, and quantum information.
Zhenda Xie is a professor at Nanjing University, School of Electronic Science and Engineering. He received his PhD degree at Nanjing University in 2011, and worked as postdoctoral research scientist and senior research scientist at Columbia University and UCLA from 2011 to 2016. His research focus on optical microstructures, quantum optics, and nonlinear optics. He has published over 80 papers in high impact journal, including National Science Review, Nature Photonics, Physical Review Letters, Light: Science & Applications, and Nature Communications.
Shining Zhu is a professor at the School of Physics and at the National Laboratory of Solid State Microstructures, Nanjing University, China. He is also an academician of the Chinese Academy of Sciences, and a fellow of OSA, COS, and APS. He got his master’s and PhD degrees from the Physics Department of Nanjing University. Since then he has been working on functionally microstructured materials, paying close attention to their applications in laser, nonlinear, and quantum optics. He and his collaborators have published more than 600 papers in SCI journals, including Science, Nature, Physical Review Letters, and Advanced Photonics.
Biographies of the other authors are not available.
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Hua-Ying Liu, Minghao Shang, Xiaoyi Liu, Ying Wei, Minghao Mi, Lijian Zhang, Yan-Xiao Gong, Zhenda Xie, Shining Zhu. Deterministic N-photon state generation using lithium niobate on insulator device[J]. Advanced Photonics Nexus, 2023, 2(1): 016003
Category: Research Articles
Received: Aug. 11, 2022
Accepted: Nov. 10, 2022
Published Online: Dec. 16, 2022
The Author Email: Liu Hua-Ying (liuhuaying@nju.edu.cn), Gong Yan-Xiao (gongyanxiao@nju.edu.cn), Xie Zhenda (xiezhenda@nju.edu.cn)