Abstract
Soliton microcombsâphase-locked microcavity frequency combsâhave become the foundation of several classical technologies in integrated photonics, including spectroscopy, LiDAR and optical computing. Despite the predicted multimode entanglement across the comb, experimental study of the quantum optics of the soliton microcomb has been elusive. In this work we use second-order photon correlations to study the underlying quantum processes of soliton microcombs in an integrated silicon carbide microresonator. We show that a stable temporal lattice of solitons can isolate a multimode below-threshold Gaussian state from any admixture of coherent light, and predict that all-to-all entanglement can be realized for the state. Our work opens a pathway toward a soliton-based multimode quantum resource.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 /Â 30Â days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the corresponding author on request.
Code availability
The code used in this study is available from the corresponding author on request.
References
Kippenberg, T. J., Gaeta, A. L., Lipson, M. & Gorodetsky, M. L. Dissipative Kerr solitons in optical microresonators. Science 361, aan8083 (2018).
Diddams, S. A., Vahala, K. & Udem, T. Optical frequency combs: coherently uniting the electromagnetic spectrum. Science 369, aay3676 (2020).
Kues, M. et al. Quantum optical microcombs. Nat. Photon. 13, 170â179 (2019).
Grassani, D. et al. Micrometer-scale integrated silicon source of time-energy entangled photons. Optica 2, 88â94 (2015).
Jaramillo-Villegas, J. A. et al. Persistent energyâtime entanglement covering multiple resonances of an on-chip biphoton frequency comb. Optica 4, 655â658 (2017).
Steiner, T. J. et al. Ultra-bright entangled-photon pair generation from an AlGaAs-on-insulator microring resonator. PRX Quantum 2, 010337 (2021).
Reimer, C. et al. Generation of multiphoton entangled quantum states by means of integrated frequency combs. Science 351, 1176â1180 (2016).
Kues, M. et al. On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature 546, 622â626 (2017).
Samara, F. et al. Entanglement swapping between independent and asynchronous integrated photon-pair sources. Quantum Sci. Technol. 6, 045024 (2021).
Vaidya, V. D. et al. Broadband quadrature-squeezed vacuum and nonclassical photon number correlations from a nanophotonic device. Sci. Adv. 6, eaba9186 (2020).
Zhao, Y. et al. Near-degenerate quadrature-squeezed vacuum generation on a silicon-nitride chip. Phys. Rev. Lett. 124, 193601 (2020).
Arrazola, J. et al. Quantum circuits with many photons on a programmable nanophotonic chip. Nature 591, 54â60 (2021).
Suh, M.-G., Yang, Q.-F., Yang, K. Y., Yi, X. & Vahala, K. J. Microresonator soliton dual-comb spectroscopy. Science 354, 600â603 (2016).
Riemensberger, J. et al. Massively parallel coherent laser ranging using a soliton microcomb. Nature 581, 164â170 (2020).
Spencer, D. T. et al. An optical-frequency synthesizer using integrated photonics. Nature 557, 81â85 (2018).
Feldmann, J. et al. Parallel convolutional processing using an integrated photonic tensor core. Nature 589, 52â58 (2021).
Roslund, J., De Araujo, R. M., Jiang, S., Fabre, C. & Treps, N. Wavelength-multiplexed quantum networks with ultrafast frequency combs. Nat. Photon. 8, 109â112 (2014).
Cai, Y. et al. Multimode entanglement in reconfigurable graph states using optical frequency combs. Nat. Commun. 8, 1â9 (2017).
Chen, M., Menicucci, N. C. & Pfister, O. Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb. Phys. Rev. Lett. 112, 120505 (2014).
Pfister, O. Continuous-variable quantum computing in the quantum optical frequency comb. J. Phys. B 53, 012001 (2019).
Wang, J., Sciarrino, F., Laing, A. & Thompson, M. G. Integrated photonic quantum technologies. Nat. Photon. 14, 273â284 (2020).
Wu, B.-H., Alexander, R. N., Liu, S. & Zhang, Z. Quantum computing with multidimensional continuous-variable cluster states in a scalable photonic platform. Phys. Rev. Res. 2, 023138 (2020).
Tasker, J. F. et al. Silicon photonics interfaced with integrated electronics for 9 GHz measurement of squeezed light. Nat. Photon. 15, 11â15 (2021).
Yang, Z. et al. A squeezed quantum microcomb on a chip. Nat. Photon. 12, 1â8 (2021).
Xie, Z. et al. Harnessing high-dimensional hyperentanglement through a biphoton frequency comb. Nat. Photon. 9, 536â542 (2015).
Asavanant, W. et al. Generation of time-domain-multiplexed two-dimensional cluster state. Science 366, 373â376 (2019).
Larsen, M. V., Guo, X., Breum, C. R., Neergaard-Nielsen, J. S. & Andersen, U. L. Deterministic generation of a two-dimensional cluster state. Science 366, 369â372 (2019).
Zhong, H.-S. et al. Quantum computational advantage using photons. Science 370, 1460â1463 (2020).
Matsko, A. B. & Maleki, L. On timing jitter of mode locked Kerr frequency combs. Opt. Express 21, 28862â28876 (2013).
Bao, C. et al. Quantum diffusion of microcavity solitons. Nat. Phys. 17, 462â466 (2021).
Chembo, Y. K. Quantum dynamics of kerr optical frequency combs below and above threshold: spontaneous four-wave mixing, entanglement, and squeezed states of light. Phys. Rev. A 93, 033820 (2016).
Chembo, Y. K. & Menyuk, C. R. Spatiotemporal LugiatoâLefever formalism for Kerr-comb generation in whispering-gallery-mode resonators. Phys. Rev. A 87, 053852 (2013).
Haus, H. A. & Lai, Y. Quantum theory of soliton squeezing: a linearized approach. JOSA B 7, 386â392 (1990).
Spälter, S., Korolkova, N., König, F., Sizmann, A. & Leuchs, G. Observation of multimode quantum correlations in fiber optical solitons. Phys. Rev. Lett. 81, 786 (1998).
Navarrete-Benlloch, C., Roldán, E., Chang, Y. & Shi, T. Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators. Opt. Express 22, 24010â24023 (2014).
Vernon, Z. & Sipe, J. Strongly driven nonlinear quantum optics in microring resonators. Phys. Rev. A 92, 033840 (2015).
Cole, D. C., Lamb, E. S., DelâHaye, P., Diddams, S. A. & Papp, S. B. Soliton crystals in Kerr resonators. Nat. Photon. 11, 671â676 (2017).
Karpov, M. et al. Dynamics of soliton crystals in optical microresonators. Nat. Phys. 15, 1071â1077 (2019).
Guidry, M. A. et al. Optical parametric oscillation in silicon carbide nanophotonics. Optica 7, 1139â1142 (2020).
Lukin, D. M. et al. 4H-silicon-carbide-on-insulator for integrated quantum and nonlinear photonics. Nat. Photon. 14, 330â334 (2020).
Ou, Z. & Lu, Y. Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons. Phys. Rev. Lett. 83, 2556 (1999).
Blauensteiner, B., Herbauts, I., Bettelli, S., Poppe, A. & Hübel, H. Photon bunching in parametric down-conversion with continuous-wave excitation. Phys. Rev. A 79, 063846 (2009).
Herr, T. et al. Universal formation dynamics and noise of Kerr-frequency combs in microresonators. Nat. Photon. 6, 480â487 (2012).
Coillet, A. et al. On the transition to secondary Kerr combs in whispering-gallery mode resonators. Opt. Lett. 44, 3078â3081 (2019).
da Silva, T. F., do Amaral, G. C., Vitoreti, D., Temporão, G. P. & von der Weid, J. P. Spectral characterization of weak coherent state sources based on two-photon interference. JOSA B 32, 545â549 (2015).
Navarrete-Benlloch, C., Garcés, R., Mohseni, N. & de Valcárcel, G. Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: application to squeezed parametric oscillation beyond the rotating-wave approximation. Phys. Rev. A 103, 023713 (2021).
Lukin, D. M. et al. Spectrally reconfigurable quantum emitters enabled by optimized fast modulation. npj Quant. Info. 6, 1â9 (2020).
Vidal, G. & Werner, R. F. Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002).
Zhang, M. et al. Electronically programmable photonic molecule. Nat. Photon. 13, 36â40 (2019).
Helgason, Ã. B. et al. Dissipative solitons in photonic molecules. Nat. Photon. 15, 305â310 (2021).
Ra, Y.-S. et al. Non-gaussian quantum states of a multimode light field. Nat. Phys. 16, 144â147 (2020).
Brasch, V. et al. Photonic chipâbased optical frequency comb using soliton Cherenkov radiation. Science 351, 357â360 (2016).
Lu, X. et al. Chip-integrated visibleâtelecom entangled photon pair source for quantum communication. Nat. Phys. 15, 373â381 (2019).
Jin, W. et al. Hertz-linewidth semiconductor lasers using CMOS-ready ultra-high-Q microresonators. Nat. Photon. 15, 346â353 (2021).
Xiang, C. et al. Laser soliton microcombs heterogeneously integrated on silicon. Science 373, 99â103 (2021).
Hu, Y. et al. On-chip electro-optic frequency shifters and beam splitters. Nature 599, 587â593 (2021).
Daugey, T., Billet, C., Dudley, J., Merolla, J.-M. & Chembo, Y. K. Kerr optical frequency comb generation using whispering-gallery-mode resonators in the pulsed-pump regime. Phys. Rev. A 103, 023521 (2021).
Imany, P., Lingaraju, N. B., Alshaykh, M. S., Leaird, D. E. & Weiner, A. M. Probing quantum walks through coherent control of high-dimensionally entangled photons. Sci. Adv. 6, eaba8066 (2020).
Bruch, A. W. et al. Pockels soliton microcomb. Nat. Photon. 15, 21â27 (2021).
Moille, G. et al. Kerr-microresonator soliton frequency combs at cryogenic temperatures. Phys. Rev. Appl. 12, 034057 (2019).
Acknowledgements
We gratefully acknowledge discussions with J. Bowers, T. Zhong, L. Chang, C. Bao, B. Shen, A. Dutt and S. Sun. This work is funded by the Defense Advanced Research Projects Agency under the PIPES and LUMOS programmes and by the IET AF Harvey Prize. M.A.G. acknowledges the Albion Hewlett Stanford Graduate Fellowship (SGF) and the NSF Graduate Research Fellowship. D.M.L. acknowledges the Fong SGF and the National Defense Science and Engineering Graduate Fellowship. Part of this work was performed at the Stanford Nanofabrication Facility (SNF) and the Stanford Nano Shared Facilities (SNSF).
Author information
Authors and Affiliations
Contributions
M.A.G., D.M.L., K.Y.Y. and J.V. conceived the experiment. M.A.G. conducted quantum correlations theory. K.Y.Y, M.A.G. and D.M.L. conducted soliton generation experiments. D.M.L, M.A.G. and K.Y.Y. conducted quantum correlations experiments. D.M.L. fabricated the devices. D.M.L., K.Y.Y. and M.A.G. conducted LLE simulations. M.A.G. and R.T. performed the entanglement calculation. R.T. provided theoretical guidance. J.V. supervised the project. All authors discussed the results and contributed to the final manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Peer review information Nature Photonics thanks the anonymous reviewers for their contribution to the peer review of this work.
Publisherâs note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Supplementary Figs. 1â7, Discussion and Table 1.
Rights and permissions
About this article
Cite this article
Guidry, M.A., Lukin, D.M., Yang, K.Y. et al. Quantum optics of soliton microcombs. Nat. Photon. 16, 52â58 (2022). https://doi.org/10.1038/s41566-021-00901-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41566-021-00901-z
This article is cited by
-
An integrated 3C-silicon carbide-on-insulator photonic platform for nonlinear and quantum light sources
Communications Physics (2024)
-
Integrated vortex soliton microcombs
Nature Photonics (2024)
-
Parametrically driven pure-Kerr temporal solitons in a chip-integrated microcavity
Nature Photonics (2024)
-
Silicon carbide, the next-generation integrated platform for quantum technology
Light: Science & Applications (2024)
-
Nonlinear and quantum photonics using integrated optical materials
Nature Reviews Materials (2024)