Quantum prospects for hybrid thin-film lithium niobate on silicon photonics

Abstract

Photonics is poised to play a unique role in quantum technology for computation, communications and sensing. Meanwhile, integrated photonic circuits—with their intrinsic phase stability and high-performance, nanoscale components—offer a route to scaling. However, each integrated platform has a unique set of advantages and pitfalls, which can limit their power. So far, the most advanced demonstrations of quantum photonic circuitry has been in silicon photonics. However, thin-film lithium niobate (TFLN) is emerging as a powerful platform with unique capabilities; advances in fabrication have yielded loss metrics competitive with any integrated photonics platform, while its large second-order nonlinearity provides efficient nonlinear processing and ultra-fast modulation. In this short review, we explore the prospects of dynamic quantum circuits—such as multiplexed photon sources and entanglement generation—on hybrid TFLN on silicon (TFLN/Si) photonics and argue that hybrid TFLN/Si photonics may have the capability to deliver the photonic quantum technology of tomorrow.

Graphical abstract

Keywords

Quantum photonics / Quantum information / Quantum communications / Lithium niobate (LN) / Silicon photonics

References

[1] Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018)

[2] Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., Brandao, F.G.S.L., Buell, D.A., Burkett, B., Chen, Y., Chen, Z., Chiaro, B., Collins, R., Courtney, W., Dunsworth, A., Farhi, E., Foxen, B., Fowler, A., Gidney, C., Giustina, M., Graff, R., Guerin, K., Habegger, S., Harrigan, M.P., Hartmann, M.J., Ho, A., Hoffmann, M., Huang, T., Humble, T.S., Isakov, S.V., Jeffrey, E., Jiang, Z., Kafri, D., Kechedzhi, K., Kelly, J., Klimov, P.V., Knysh, S., Korotkov, A., Kostritsa, F., Landhuis, D., Lindmark, M., Lucero, E., Lyakh, D., Mandrà, S., McClean, J.R., McEwen, M., Megrant, A., Mi, X., Michielsen, K., Mohseni, M., Mutus, J., Naaman, O., Neeley, M., Neill, C., Niu, M.Y., Ostby, E., Petukhov, A., Platt, J.C., Quintana, C., Rieffel, E.G., Roushan, P., Rubin, N.C., Sank, D., Satzinger, K.J., Smelyanskiy, V., Sung, K.J., Trevithick, M.D., Vainsencher, A., Villalonga, B., White, T., Yao, Z.J., Yeh, P., Zalcman, A., Neven, H., Martinis, J.M.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)

[3] Zhong, H.S., Deng, Y.H., Qin, J., Wang, H., Chen, M.C., Peng, L.C., Luo, Y.H., Wu, D., Gong, S.Q., Su, H., Hu, Y.: Phase-programmable gaussian boson sampling using stimulated squeezed light. arxiv preprint arxiv: 2106. 15534 (2021)

[4] Wu, Y.L., Bao, W.S., Cao, S.R., Chen, F.S., Chen, M.C., Chen, X.W., Chung, T.S., Deng, H., Du, Y.J., Fan, D.J., Gong, M., Guo, C., Guo, C., Guo, S.J., Han, L.C., Hong, L.Y., Huang, H.L., Huo, Y.H., Li, L.P., Li, N., Li, S.W., Li, Y., Liang, F.T., Lin, C., Lin, J., Qian, H.R., Qiao, D., Rong, H., Su, H., Sun, L.H., Wang, L.Y., Wang, S.Y., Wu, D.C., Xu, Y., Yan, K., Yang, W.F., Yang, Y., Ye, Y.S., Yin, J.H., Ying, C., Yu, J.L., Zha, C., Zhang, C., Zhang, H.B., Zhang, K.L., Zhang, Y.M., Zhao, H., Zhao, Y.W., Zhou, L., Zhu, Q.L., Lu, C.Y., Peng, C.Z., Zhu, X.B., Pan, J.W.: Strong quantum computational advantage using a superconducting quantum processor. Phys. Rev. Lett. 127(18), 180501 (2021)

[5] Liao, S.K., Cai, W.Q., Liu, W.Y., Zhang, L., Li, Y., Ren, J.G., Yin, J., Shen, Q., Cao, Y., Li, Z.P., Li, F.Z., Chen, X.W., Sun, L.H., Jia, J.J., Wu, J.C., Jiang, X.J., Wang, J.F., Huang, Y.M., Wang, Q., Zhou, Y.L., Deng, L., Xi, T., Ma, L., Hu, T., Zhang, Q., Chen, Y.A., Liu, N.L., Wang, X.B., Zhu, Z.C., Lu, C.Y., Shu, R., Peng, C.Z., Wang, J.Y., Pan, J.W.: Satellite-to-ground quantum key distribution. Nature 549(7670), 43–47 (2017)

[6] Ren, J.G., Xu, P., Yong, H.L., Zhang, L., Liao, S.K., Yin, J., Liu, W.Y., Cai, W.Q., Yang, M., Li, L., Yang, K.X., Han, X., Yao, Y.Q., Li, J., Wu, H.Y., Wan, S., Liu, L., Liu, D.Q., Kuang, Y.W., He, Z.P., Shang, P., Guo, C., Zheng, R.H., Tian, K., Zhu, Z.C., Liu, N.L., Lu, C.Y., Shu, R., Chen, Y.A., Peng, C.Z., Wang, J.Y., Pan, J.W.: Ground-to-satellite quantum teleportation. Nature 549(7670), 70–73 (2017)

[7] Giustina, M., Versteegh, M.A.M., Wengerowsky, S., Handsteiner, J., Hochrainer, A., Phelan, K., Steinlechner, F., Kofler, J., Larsson, J., Abellán, C., Amaya, W., Pruneri, V., Mitchell, M.W., Beyer, J., Gerrits, T., Lita, A.E., Shalm, L.K., Nam, S.W., Scheidl, T., Ursin, R., Wittmann, B., Zeilinger, A.: Significant-loophole-free test of Bell’s theorem with entangled photons. Phys. Rev. Lett. 115(25), 250401 (2015)

[8] Hensen, B., Bernien, H., Dréau, A.E., Reiserer, A., Kalb, N., Blok, M.S., Ruitenberg, J., Vermeulen, R.F., Schouten, R.N., Abellán, C., Amaya, W., Pruneri, V., Mitchell, M.W., Markham, M., Twitchen, D.J., Elkouss, D., Wehner, S., Taminiau, T.H., Hanson, R.: Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526(7575), 682–686 (2015)

[9] Shalm, L.K., Meyer-Scott, E., Christensen, B.G., Bierhorst, P., Wayne, M.A., Stevens, M.J., Gerrits, T., Glancy, S., Hamel, D.R., Allman, M.S., Coakley, K.J., Dyer, S.D., Hodge, C., Lita, A.E., Verma, V.B., Lambrocco, C., Tortorici, E., Migdall, A.L., Zhang, Y., Kumor, D.R., Farr, W.H., Marsili, F., Shaw, M.D., Stern, J.A., Abellán, C., Amaya, W., Pruneri, V., Jennewein, T., Mitchell, M.W., Kwiat, P.G., Bienfang, J.C., Mirin, R.P., Knill, E., Nam, S.W.: Strong loophole-free test of local realism. Phys. Rev. Lett. 115(25), 250402 (2015)

[10] Bromley, T.R., Arrazola, J.M., Jahangiri, S., Izaac, J., Quesada, N., Gran, A.D., Schuld, M., Swinarton, J., Zabaneh, Z., Killoran, N.: Applications of near-term photonic quantum computers: software and algorithms. Quan. Sci. Technol. 5(3), 034010 (2020)

[11] Wang, J., Sciarrino, F., Laing, A., Thompson, M.G.: Integrated photonic quantum technologies. Nat. Photon. 14(5), 273–284 (2020)

[12] Silverstone, J.W., Wang, J., Bonneau, D., Sibson, P., Santagati, R., Erven, C., O'Brien, J.L., Thompson, M.G.: Silicon quantum photonics. In: Proceedings of International Conference on Optical MEMS and Nanophotonics (OMN). Singapore: IEEE (2016)

[13] Adcock, J.C., Bao, J., Chi, Y., Chen, X., Bacco, D., Gong, Q., Oxenlowe, L.K., Wang, J., Ding, Y.: Advances in silicon quantum photonics. IEEE J. Sel. Top. Quantum Electron. 27(2), 1–24 (2021)

[14] Sibson, P., Kennard, J.E., Stanisic, S., Erven, C., O’Brien, J.L., Thompson, M.G.: Integrated silicon photonics for high-speed quantum key distribution. Optica 4(2), 172–177 (2017)

[15] Llewellyn, D., Ding, Y., Faruque, I.I., Paesani, S., Bacco, D., Santagati, R., Qian, Y.J., Li, Y., Xiao, Y.F., Huber, M., Malik, M., Sinclair, G.F., Zhou, X., Rottwitt, K., O’Brien, J.L., Rarity, J.G., Gong, Q., Oxenlowe, L.K., Wang, J., Thompson, M.G.: Chip-to-chip quantum teleportation and multi-photon entanglement in silicon. Nat. Phys. 16(2), 148–153 (2020)

[16] Vigliar, C., Paesani, S., Ding, Y.H., Adcock, J.C., Wang, J.W., Morley-Short, S., Bacco, D., Oxenløwe, L.K., Thompson, M.G., Rarity, J.G., Laing, A.: Error protected qubits in a silicon photonic chip. Nat. Phys. 17(10), 1137–1143 (2020)

[17] Paesani, S., Ding, Y., Santagati, R., Chakhmakhchyan, L., Vigliar, C., Rottwitt, K., Oxenløwe, L.K., Wang, J., Thompson, M.G., Laing, A.: Generation and sampling of quantum states of light in a silicon chip. Nat. Phys. 15(9), 925–929 (2019)

[18] Ono, T., Sinclair, G.F., Bonneau, D., Thompson, M.G., Matthews, J.C.F., Rarity, J.G.: Observation of nonlinear interference on a silicon photonic chip. Opt. Lett. 44(5), 1277–1280 (2019)

[19] Rudolph, T.: Why I am optimistic about the silicon-photonic route to quantum computing. APL Photon. 2(3), 030901 (2017)

[20] Levy, M., Osgood, R.M., Liu, R., Cross, L.E., Cargill, G.S.I.I.I., Kumar, A., Bakhru, H.: Fabrication of single-crystal lithium niobate films by crystal ion slicing. Appl. Phys. Lett. 73(16), 2293– 2295 (1998)

[21] Rabiei, P., Ma, J., Khan, S., Chiles, J., Fathpour, S.: Heterogeneous lithium niobate photonics on silicon substrates. Opt. Express 21(21), 25573–25581 (2013)

[22] Poberaj, G., Hu, H., Sohler, W., Günter, P.: Lithium niobate on insulator (LNOI) for micro-photonic devices. Laser Photonics Rev. 6(4), 488–503 (2012)

[23] Bazzan, M., Sada, C.: Optical waveguides in lithium niobate: recent developments and applications. Appl. Phys. Rev. 2(4), 040603 (2015)

[24] Weigel, P.O., Zhao, J., Fang, K., Al-Rubaye, H., Trotter, D., Hood, D., Mudrick, J., Dallo, C., Pomerene, A.T., Starbuck, A.L., DeRose, C.T., Lentine, A.L., Rebeiz, G., Mookherjea, S.: Bonded thin film lithium niobate modulator on a silicon photonics platform exceeding 100 GHz 3-dB electrical modulation bandwidth. Opt. Express 26(18), 23728–23739 (2018)

[25] Sakashita, Y., Segawa, H.: Preparation and characterization of LiNbO3 thin films produced by chemical-vapor deposition. J. Appl. Phys. 77(11), 5995–5999 (1995)

[26] Nakata, Y., Gunji, S., Okada, T., Maeda, M.: Fabrication of LiNbO3 thin films by pulsed laser deposition and investigation of nonlinear properties. Appl. Phys. A 79(4–6), 1279–1282 (2004)

[27] Gitmans, F., Sitar, Z., Günter, P.: Growth of tantalum oxide and lithium tantalate thin films by molecular beam epitaxy. Vacuum 46(8–10), 939–942 (1995)

[28] Lansiaux, X., Dogheche, E., Remiens, D., Guilloux-viry, M., Perrin, A., Ruterana, P.: LiNbO3 thick films grown on sapphire by using a multistep sputtering process. J. Appl. Phys. 90(10), 5274–5277 (2001)

[29] Bruel, M.: Silicon on insulator material technology. Electron. Lett. 31(14), 1201–1202 (1995)

[30] Mercante, A.J., Yao, P., Shi, S., Schneider, G., Murakowski, J., Prather, D.W.: 110 GHz CMOS compatible thin film LiNbO₃ modulator on silicon. Opt. Express 24(14), 15590–15595 (2016)

[31] Wang, C., Zhang, M., Chen, X., Bertrand, M., Shams-Ansari, A., Chandrasekhar, S., Winzer, P., Lončar, M.: Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages. Nature 562(7725), 101–104 (2018)

[32] Wang, C., Zhang, M., Stern, B., Lipson, M., Lončar, M.: Nanophotonic lithium niobate electro-optic modulators. Opt. Express 26(2), 1547–1555 (2018)

[33] He, M., Xu, M., Ren, Y., Jian, J., Ruan, Z., Xu, Y., Gao, S., Sun, S., Wen, X., Zhou, L., Liu, L., Guo, C., Chen, H., Yu, S., Liu, L., Cai, X.: High-performance hybrid silicon and lithium niobate Mach-Zehnder modulators for 100 Gbit s−1 and beyond. Nat. Photonics 13(5), 359–364 (2019)

[34] Zhang, M., Wang, C., Cheng, R., Shams-Ansari, A., Lončar, M.: Monolithic ultra-high-Q lithium niobate microring resonator. Optica 4(12), 1536–1537 (2017)

[35] Zhang, M., Wang, C., Hu, Y., Shams-Ansari, A., Ren, T., Fan, S., Lončar, M.: Electronically programmable photonic molecule. Nat. Photonics 13(1), 36–40 (2019)

[36] Wang, C., Zhang, M., Yu, M., Zhu, R., Hu, H., Loncar, M.: Monolithic lithium niobate photonic circuits for Kerr frequency comb generation and modulation. Nat. Commun. 10(1), 978 (2019)

[37] Xu, M., He, M., Zhang, H., Jian, J., Pan, Y., Liu, X., Chen, L., Meng, X., Chen, H., Li, Z., Xiao, X., Yu, S., Yu, S., Cai, X.: High-performance coherent optical modulators based on thin-film lithium niobate platform. Nat. Commun. 11(1), 3911 (2020)

[38] Pohl, D., Reig Escalé, M., Madi, M., Kaufmann, F., Brotzer, P., Sergeyev, A., Guldimann, B., Giaccari, P., Alberti, E., Meier, U., Grange, R.: An integrated broadband spectrometer on thin-film lithium niobate. Nat. Photonics 14(1), 24–29 (2020)

[39] Sun, D., Zhang, Y., Wang, D., Song, W., Liu, X., Pang, J., Geng, D., Sang, Y., Liu, H.: Microstructure and domain engineering of lithium niobate crystal films for integrated photonic applications. Light Sci. Appl. 9(1), 197 (2020)

[40] Li, H., Ma, B.: Research development on fabrication and optical properties of nonlinear photonic crystals. Front. Optoelectron. 13(1), 35–49 (2020)

[41] Chen, F.: Laser-written three dimensional nonlinear photonic crystals. Front. Optoelectron. 12(4), 342–343 (2019)

[42] Lu, J., Surya, J.B., Liu, X., Bruch, A.W., Gong, Z., Xu, Y., Tang, H.X.: Periodically poled thin-film lithium niobate microring resonators with a second-harmonic generation efficiency of 250000%/W. Optica 6(12), 1455–1460 (2019)

[43] Liu, X., Ying, P., Zhong, X., Xu, J., Han, Y., Yu, S., Cai, X.: Highly efficient thermo-optic tunable micro-ring resonator based on an LNOI platform. Opt. Lett. 45(22), 6318–6321 (2020)

[44] Thomson, D., Zilkie, A., Bowers, J.E., Komljenovic, T., Reed, G.T., Vivien, L., Marris-Morini, D., Cassan, E., Virot, L., Fédéli, J.M., Hartmann, J.M., Schmid, J.H., Xu, D.X., Boeuf, F., O’Brien, P., Mashanovich, G.Z., Nedeljkovic, M.: Roadmap on silicon photonics. J. Opt. 18(7), 073003 (2016)

[45] Treyz, G.V., May, P.G., Halbout, J.M.: Silicon Mach-Zehnder waveguide interferometers based on the plasma dispersion effect. Appl. Phys. Lett. 59(7), 771–773 (1991)

[46] Liu, A., Liao, L., Rubin, D., Nguyen, H., Ciftcioglu, B., Chetrit, Y., Izhaky, N., Paniccia, M.: High-speed optical modulation based on carrier depletion in a silicon waveguide. Opt. Express 15(2), 660–668 (2007)

[47] Ding, Y., Peucheret, C., Ou, H., Yvind, K.: Fully etched apodized grating coupler on the SOI platform with −0.58 dB coupling efficiency. Opt. Lett. 39(18), 5348–5350 (2014)

[48] Notaros, J., Pavanello, F., Wade, M. T., Gentry, C. M., Atabaki, A., Alloatti, L., Ram, R. J., Miloš, A. P. Ultra-efficient CMOS fiber-to-chip grating couplers. In: Proceedings of Optical Fiber Communications Conference and Exhibition (OFC). Anaheim: IEEE (2016)

[49] Hoppe, N., Zaoui, W.S., Rathgeber, L., Wang, Y., Klenk, R.H., Vogel, W., Kaschel, M., Portalupi, S.L., Burghartz, J., Berroth, M.: Ultra-efficient silicon-on-insulator grating couplers with backside metal mirrors. IEEE J. Sel. Top. Quantum Electron. 26(2), 1–6 (2020)

[50] Horikawa, T., Shimura, D., Mogami, T.: Low-loss silicon wire waveguides for optical integrated circuits. MRS Commun. 6(1), 9–15 (2016)

[51] Biberman, A., Shaw, M.J., Timurdogan, E., Wright, J.B., Watts, M.R.: Ultralow-loss silicon ring resonators. Opt. Lett. 37(20), 4236–4238 (2012)

[52] Liu, Y., Wu, C., Gu, X., Kong, Y., Yu, X., Ge, R., Cai, X., Qiang, X., Wu, J., Yang, X., Xu, P.: High-spectral-purity photon generation from a dual-interferometer-coupled silicon microring. Opt. Lett. 45(1), 73–76 (2020)

[53] Paesani, S., Borghi, M., Signorini, S., Maïnos, A., Pavesi, L., Laing, A.: Near-ideal spontaneous photon sources in silicon quantum photonics. Nat. Commun. 11(1), 2505 (2020)

[54] Christensen, J.B., Koefoed, J.G., Rottwitt, K., McKinstrie, C.: Engineering spectrally unentangled photon pairs from nonlinear microring resonators through pump manipulation. arxiv preprint arxiv: 1711. 02401 (2017)

[55] Vernon, Z., Menotti, M., Tison, C.C., Steidle, J.A., Fanto, M.L., Thomas, P.M., Preble, S.F., Smith, A.M., Alsing, P.M., Liscidini, M., Sipe, J.E.: Truly unentangled photon pairs without spectral filtering. Opt. Lett. 42(18), 3638–3641 (2017)

[56] Zhu, H., Li, Q., Han, H., Li, Z., Zhang, X., Zhang, H., Hu, H.: Hybrid mono-crystalline silicon and lithium niobate thin films. Chin. Opt. Lett. 19, 060017 (2021)

[57] Weigel, P.O., Savanier, M., DeRose, C.T., Pomerene, A.T., Starbuck, A.L., Lentine, A.L., Stenger, V., Mookherjea, S.: Lightwave circuits in lithium niobate through hybrid waveguides with silicon photonics. Sci. Rep. 6(1), 22301 (2016)

[58] Krasnokutska, I., Chapman, R.J., Tambasco, J.J., Peruzzo, A.: High coupling efficiency grating couplers on lithium niobate on insulator. Opt. Express 27(13), 17681–17685 (2019)

[59] Chen, B., Ruan, Z., Hu, J., Wang, J., Lu, C., Lau, A.P.T., Guo, C., Chen, K., Chen, P., Liu, L.: Two-dimensional grating coupler on an X-cut lithium niobate thin-film. Opt. Express 29(2), 1289–1295 (2021)

[60] Ruan, Z., Hu, J., Xue, Y., Liu, J., Chen, B., Wang, J., Chen, K., Chen, P., Liu, L.: Metal based grating coupler on a thin-film lithium niobate waveguide. Opt. Express 28(24), 35615–35621 (2020)

[61] Bowers, J. E., Liu, A. Y. A comparison of four approaches to photonic integration. In: Proceedings of Optical Fiber Communication Conference. Los Angeles: IEEE (2017)

[62] Ogiso, Y., Ozaki, J., Ueda, Y., Kashio, N., Kikuchi, N., Yamada, E., Tanobe, H., Kanazawa, S., Yamazaki, H., Ohiso, Y., Fujii, T., Kohtoku, M.: Over 67 GHz bandwidth and 15 V Vπ InP-based optical IQ modulator with nipn heterostructure. J. Lightwave Technol. 35(8), 1450–1455 (2017)

[63] Ottaviano, L., Pu, M., Semenova, E., Yvind, K.: Low-loss high-confinement waveguides and microring resonators in AlGaAs-on-insulator. Opt. Lett. 41(17), 3996–3999 (2016)

[64] Burla, M., Hoessbacher, C., Heni, W., Haffner, C., Fedoryshyn, Y., Werner, D., Watanabe, T., Massler, H., Elder, D., Dalton, L., Leuthold, J.: 500 GHz plasmonic Mach-Zehnder modulator enabling sub-THz microwave photonics. APL Photon. 4(5), 056106 (2019)

[65] Zhong, C., Li, J., Lin, H.: Graphene-based all-optical modulators. Front. Optoelectron. 13(2), 114–128 (2020)

[66] Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409(6816), 46–52 (2001)

[67] Bartolucci, S., Birchall, P., Bombin, H., Cable, H., Dawson, C., Gimeno-Segovia, M., Johnston, E., Kieling, K., Nickerson, N., Pant, M., Pastawski, F., Rudolph, T., Sparrow, C.: Fusion-based quantum computation. arxiv preprint arxiv: 2101. 09310 (2021)

[68] Takeda, S., Furusawa, A.: Toward large-scale fault-tolerant universal photonic quantum computing. APL Photon. 4(6), 060902 (2019)

[69] Bourassa, J.E., Alexander, R.N., Vasmer, M., Patil, A., Tzitrin, I., Matsuura, T., Su, D., Baragiola, B.Q., Guha, S., Dauphinais, G., Sabapathy, K.K., Menicucci, N.C., Dhand, I.: Blueprint for a scalable photonic fault-tolerant quantum computer. Quantum 5, 392 (2021)

[70] Azuma, K., Tamaki, K., Lo, H.K.: All-photonic quantum repeaters. Nat. Commun. 6(1), 6787 (2015)

[71] Adcock, J.C., Morley-Short, S., Silverstone, J.W., Thompson, M.G.: Hard limits on the postselectability of optical graph states. Quan. Sci. Technol. 4, 015010 (2018)

[72] Migdall, A.L., Branning, D., Castelletto, S.: Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source. Phys. Rev. A 66(5), 053805 (2002)

[73] Pittman, T.B., Jacobs, B.C., Franson, P.: Single photons on pseudodemand from stored parametric down-conversion. Phys. Rev. A 66(4), 042303 (2002)

[74] Bonneau, D., Mendoza, G.J., O’Brien, J.L., Thompson, M.G.: Effect of loss on multiplexed single-photon sources. New J. Phys. 17(4), 043057 (2015)

[75] Fumihiro, K., Kwiat, P.: High-efficiency single-photon generation via large-scale active time multiplexing. Sci. Adv. 5(10), eaaw8586 (2019)

[76] Collins, M.J., Xiong, C., Rey, I.H., Vo, T.D., He, J., Shahnia, S., Reardon, C., Krauss, T.F., Steel, M.J., Clark, A.S., Eggleton, B.J.: Integrated spatial multiplexing of heralded single-photon sources. Nat. Commun. 4(1), 2582 (2013)

[77] Joshi, C., Farsi, A., Clemmen, S., Ramelow, S., Gaeta, A.L.: Frequency multiplexing for quasi-deterministic heralded singlephoton sources. Nat. Commun. 9(1), 847 (2018)

[78] Thomas, S., Billard, M., Coste, N., Wein, S., Ollivier, P., Krebs, O., Tazaïrt, L., Harouri, A., Lemaitre, A., Sagnes, I., Anton, C., Lanco, L., Somaschi, N., Loredo, J., Senellart, P.: Bright polarized single-photon source based on a linear dipole. Phys. Rev. Lett. 126(23), 233601 (2021)

[79] Tomm, N., Javadi, A., Antoniadis, N.O., Najer, D., Löbl, M.C., Korsch, A.R., Schott, R., Valentin, S.R., Wieck, A.D., Ludwig, A., Warburton, R.J.: A bright and fast source of coherent single photons. Nat. Nanotechnol. 16(4), 399–403 (2021)

[80] Bartolucci, S., Birchall, P., Gimeno-Segovia, M., Johnston, E., Kieling, K., Mihir Pant, M., Rudolph, T., Smith, J., Sparrow, C., Vidrighin, M.: Creation of entangled photonic states using linear optics. arxiv preprint arxiv: 2106. 13825 (2021)

[81] Paesani, S., Bulmer, J., Jones, A., Santagati, R., Laing, A.: Scheme for universal high-dimensional quantum computation with linear optics. Phys. Rev. Lett. 126(23), 230504 (2021)

[82] Zhang, X., Bell, B., Pelusi, M., He, J., Geng, W., Kong, Y., Zhang, P., Xiong, C., Eggleton, B.J.: High repetition rate correlated photon pair generation in integrated silicon nanowires. Appl. Opt. 56(30), 8420–8424 (2017)

[83] Münzberg, J., Vetter, A., Beutel, F., Hartmann, W., Ferrari, S., Pernice, W.H.P., Rockstuhl, C.: Superconducting nanowire single- photon detector implemented in a 2D photonic crystal cavity. Optica 5(5), 658–665 (2018)

[84] Tasker J F, Frazer J, Ferranti G, Allen F, Brunel L, Tanzilli S, D’Auria V, Matthews J. 9~GHz measurement of squeezed light by interfacing silicon photonics and integrated electronics. arxiv preprint arxiv: 2009. 14318 (2020)

[85] Eltes, F., Villarreal-Garcia, G.E., Caimi, D., Siegwart, H., Gentile, A.A., Hart, A., Stark, P., Marshall, G.D., Thompson, M.G., Barreto, J., Fompeyrine, J., Abel, S.: An integrated optical modulator operating at cryogenic temperatures. Nat. Mater. 19(11), 1164–1168 (2020)

[86] Li, Y., Lan, T., Li, J., Wang, Z.: High-efficiency edge-coupling based on lithium niobate on an insulator wire waveguide. Appl. Opt. 59(22), 6694–6701 (2020)

RIGHTS & PERMISSIONS

2022 The Author(s) 2022