Coherently pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of the soliton microcombs1. Here this random walk and its impact on Kerr soliton timing jitter are studied experimentally. The quantum limit is discerned by measuring the relative position of counter-propagating solitons2. Their relative motion features weak interactions and also presents common-mode suppression of technical noise, which typically hides the quantum fluctuations. This is in contrast to co-propagating solitons, which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong correlation of their mutual motion. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multisoliton physics.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
The codes used for this study are available from the corresponding author upon reasonable request.
Matsko, A. B. & Maleki, L. On timing jitter of mode locked Kerr frequency combs. Opt. Express 21, 28862–28876 (2013).
Yang, Q.-F., Yi, X., Yang, K. Y. & Vahala, K. Counter-propagating solitons in microresonators. Nat. Photon. 11, 560–564 (2017).
Wabnitz, S. Suppression of interactions in a phase-locked soliton optical memory. Opt. Lett. 18, 601–603 (1993).
Leo, F. et al. Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer. Nat. Photon. 4, 471–476 (2010).
Herr, T. et al. Temporal solitons in optical microresonators. Nat. Photon. 8, 145–152 (2014).
Kippenberg, T., Spillane, S. & Vahala, K. Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity. Phys. Rev. Lett. 93, 083904 (2004).
Savchenkov, A. A. et al. Low threshold optical oscillations in a whispering gallery mode CaF2 resonator. Phys. Rev. Lett. 93, 243905 (2004).
Vahala, K. J. Optical microcavities. Nature 424, 839–846 (2003).
Kippenberg, T. J., Gaeta, A. L., Lipson, M. & Gorodetsky, M. L. Dissipative Kerr solitons in optical microresonators. Science 361, eaan8083 (2018).
Lucas, E. et al. Spatial multiplexing of soliton microcombs. Nat. Photon. 12, 699 (2018).
Wai, P., Menyuk, C. R., Lee, Y. & Chen, H. Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers. Opt. Lett. 11, 464–466 (1986).
Akhmediev, N. & Karlsson, M. Cherenkov radiation emitted by solitons in optical fibers. Phys. Rev. A 51, 2602–2607 (1995).
Brasch, V. et al. Photonic chip-based optical frequency comb using soliton Cherenkov radiation. Science 351, 357–360 (2016).
Yang, Q.-F., Yi, X., Yang, K. Y. & Vahala, K. Spatial-mode-interaction-induced dispersive waves and their active tuning in microresonators. Optica 3, 1132–1135 (2016).
Wang, Y. et al. Universal mechanism for the binding of temporal cavity solitons. Optica 4, 855–863 (2017).
Taheri, H., Matsko, A. B. & Maleki, L. Optical lattice trap for Kerr solitons. Eur. Phys. J. D 71, 153 (2017).
Cole, D. C., Lamb, E. S., Del’Haye, P., Diddams, S. A. & Papp, S. B. Soliton crystals in Kerr resonators. Nat. Photon. 11, 671–676 (2017).
Lugiato, L. A. & Lefever, R. Spatial dissipative structures in passive optical systems. Phys. Rev. Lett. 58, 2209–2211 (1987).
Coen, S., Randle, H. G., Sylvestre, T. & Erkintalo, M. Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato–Lefever model. Opt. Lett. 38, 37–39 (2013).
Cai, M., Painter, O. & Vahala, K. J. Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system. Phys. Rev. Lett. 85, 74–77 (2000).
Spillane, S. M., Kippenberg, T. J., Painter, O. J. & Vahala, K. J. Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics. Phys. Rev. Lett. 91, 043902 (2003).
Schibli, T. et al. Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation. Opt. Lett. 28, 947–949 (2003).
Kim, J. & Kaertner, F. X. Attosecond-precision ultrafast photonics. Laser Photon. Rev. 4, 432–456 (2010).
Bao, C. et al. Forced oscillatory motion of trapped counter-propagating solitons. Preprint at https://arxiv.org/abs/2003.00573 (2020).
Barnes, J. A. et al. Characterization of frequency stability. IEEE Trans. Instrum. Meas. 20, 105–120 (1971).
Yi, X., Yang, Q.-F., Yang, K. Y. & Vahala, K. Active capture and stabilization of temporal solitons in microresonators. Opt. Lett. 41, 2037–2040 (2016).
Rosanov, N. & Khodova, G. Diffractive autosolitons in nonlinear interferometers. J. Opt. Soc. Am. B 7, 1057–1065 (1990).
Schäpers, B., Feldmann, M., Ackemann, T. & Lange, W. Interaction of localized structures in an optical pattern-forming system. Phys. Rev. Lett. 85, 748–751 (2000).
Vladimirov, A. G., McSloy, J. M., Skryabin, D. V. & Firth, W. J. Two-dimensional clusters of solitary structures in driven optical cavities. Phys. Rev. E 65, 046606 (2002).
Vahed, H. et al. Phase-mediated long-range interactions of cavity solitons in a semiconductor laser with a saturable absorber. Phys. Rev. A 84, 063814 (2011).
Turaev, D., Vladimirov, A. & Zelik, S. Long-range interaction and synchronization of oscillating dissipative solitons. Phys. Rev. Lett. 108, 263906 (2012).
Garbin, B., Javaloyes, J., Tissoni, G. & Barland, S. Topological solitons as addressable phase bits in a driven laser. Nat. Commun. 6, 5915 (2015).
Garbin, B., Tissoni, G. & Barland, S. Excitable pulses and diffusion of localized states in a driven semiconductor laser with delay. Cybern. Phys. 7, 96–101 (2018).
Drummond, P., Shelby, R., Friberg, S. & Yamamoto, Y. Quantum solitons in optical fibres. Nature 365, 307–313 (1993).
Jeong, D. et al. Ultralow jitter silica microcomb. Optica 7, 1108–1111 (2020).
Jia, K. et al. Photonic flywheel in a monolithic fiber resonator. Phys. Rev. Lett. 125, 143902 (2020).
Paschotta, R. Noise of mode-locked lasers (part I): numerical model. Appl. Phys. B 79, 153–162 (2004).
This work is supported by the Air Force Office of Scientific Research (FA9550-18-1-0353) and the Kavli Institute of Nanoscience. C.B. acknowledges a postdoctoral fellowship from the Resnick Institute at Caltech. The work of A.B.M. was carried out at the JPL, Caltech, under a contract with the National Aeronautics and Space Administration.
The authors declare no competing interests.
Peer review information Nature Physics thanks Giovanna Tissoni and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Bao, C., Suh, MG., Shen, B. et al. Quantum diffusion of microcavity solitons. Nat. Phys. 17, 462–466 (2021). https://doi.org/10.1038/s41567-020-01152-5
Nature Physics (2021)