https://doi.org/10.1140/epjqt/s40507-026-00471-5
Research
Effects of hyperfine splitting on 1470 nm active optical clock with cesium atoms
1
National Time Service Center, Chinese Academy of Sciences, 710600, Xi’an, China
2
Key Laboratory of Time Reference and Applications, Chinese Academy of Sciences, 710600, Xi’an, China
3
School of Integrated Circuits, Peking University, 100871, Beijing, China
4
National Key Laboratory of Advanced Micro and Nano Manufacture Technology, 100871, Beijing, China
5
University of Chinese Academy of Sciences, 100049, Beijing, China
6
State Key Laboratory of Photonics and Communications, Institute of Quantum Electronics, School of Electronics, Peking University, 100871, Beijing, China
7
Hefei National Laboratory, 230088, Hefei, China
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
17
September
2025
Accepted:
16
January
2026
Published online:
27
January
2026
Abstract
Active optical clocks, benefiting from the substantially reduced cavity pulling and spectrally narrowed linewidth of bad-cavity lasers, possess the potential of simplifying clock structure and operation and facilitating broad out-of-the-lab applications. Thus far, the studies on active optical clocks with alkali-metal gain media have mainly relied on the oversimplified physical model of two-level atoms interacting with a low-Q optical cavity, omitting the effects of hyperfine splitting of the fine-structure laser transition on the clock operation. Here, we take the 1470 nm active optical clock with cesium atoms as an example and numerically investigate the clock performance in the presence of hyperfine splitting. The simulation results illustrate that multiple hyperfine laser transitions can cause a laser frequency shift at the level of hundreds of kilohertz under typical operation conditions. Nevertheless, the frequency stability may reach 
, much better than that of recently demonstrated chip-scale optical clocks. Our work shows the non-negligible influence of hyperfine splitting on the performance of active optical clocks and offers important insights for the design of future experiments.
Key words: Active optical clocks / Cavity pulling / Bad-cavity lasers / Schawlow–Townes linewidth
Deshui Yu and Baolin Zhang contributed equally to this work.
© The Author(s) 2026
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, 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 licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
