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. 2020 Aug 7;11:3975. doi: 10.1038/s41467-020-17843-9

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 4 — The rep-rate of the main solitons is stabilized by locking f_v to a Rb-referenced oscillator, and the locking is verified by using EOM method. a Rep-rate measurement using EOM method. The locking loop is engaged at the time near 50 s. The gate time (τ) is 10 ms. b Allan deviation calculated from the unlocked and locked repetition rates that are measured with the EOM method. The locking loop has ~kHz servo bandwidth. Within the servo bandwidth, the Allan deviation goes down as 1/τ. Beyond the servo bandwidth, the Allan deviation is similar to that of the free-running unlock rep-rate. The error in the rubidium clock has been corrected for the Allan deviation of the locked rep-rate. This is done by synchronizing the EOM and the soliton rep-rate to the same rubidium reference. In the entire measurement, the repetition rate of the Vernier solitons is not stabilized, and there is no feedback control of the laser-cavity detuning for the Vernier solitons.