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EPJ Quantum Technology

Effects of hyperfine splitting on 1470 nm active optical clock with cesium atoms

Deshui Yu, Baolin Zhang, Tiantian Shi, Shougang Zhang, Jingbiao Chen

Published Jan 27, 2026• 1 citation
Publisher

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 \(2.2\times 10^{-14}/\sqrt{\tau }\) , 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.

DOI
10.1140/epjqt/s40507-026-00471-5

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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 (2.2\times 10^{-14}/\sqrt{\tau }) , 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.
We experimentally demonstrate the collective emission behavior and suppressed cavity-pulling effect of four-level active optical clock with Cesium atoms. Thermal Cesium atoms in a glass cell velocity selective pumped with a 455.5 nm laser operating at 6S1/2_{1/2}1/2​ to 7P3/2_{3/2}3/2​ transition are used as lasing medium. Population inverted Cesium atoms between 7S1/2_{1/2}1/2​ and 6P3/2_{3/2}3/2​ levels are optical weakly coupled by a pair cavity mirrors working at deep bad-cavity regime with a finesse of 4.3, and the ratio between cavity bandwidth and gain bandwidth is approximately 45. With increased 455.5 nm pumping laser intensity, the output power of cesium active optical clock at 1469.9 nm from 7S1/2_{1/2}1/2​ level to 6P3/2_{3/2}3/2​ level shows a threshold and reach a power of 13 μμμW. Active optical clock would dramatically improve the optical clock stability since the lasing frequency does not follow the cavity length variation exactly, but in a form of suppressed cavity pulling effect. In this letter the cavity pulling effect is measured using a Fabry-Perot interferometer (FPI) to be reduced by a factor of 38.2 and 41.4 as the detuning between the 1469.9 nm cavity length of the Cs active optical clock and the Cs 1469.9 nm transition is set to be 140.8 MHz and 281.6 MHz respectively. The mechanism demonstrated here is of great significance for new generation optical clocks and can be applied to improve the stability of best optical clocks by at least two orders of magnitude.
We are setting up an experiment to investigate an active optical clock scheme in four-level configuration with Cesium atoms. The 1469 nm Cesium active optical clock output in a bad cavity laser regime is generated and the wavelength is measured to be 1469.500 nm by using spectrometer. The 1469 nm lasing threshold and output power is measured when changing 455 nm pumping laser power and frequency. The 1469 nm Cesium active optical clock output multi-threshold is observed when changing bad-cavity length. We also sweep the bad-cavity length and measure the 1469 nm Cesium active optical clock output frequency using a wavelength meter, proving the cavity-pulling reduction due to the bad-cavity effect.
We have experimentally demonstrated the active optical clock with a good suppression to cavity-length noise compared with the passive one. However, the frequency stability of the four-level active optical clock for thermal atoms is still limited by the residual cavity-pulling effect. In this paper, we preliminarily realized the cavity-length stabilization in 1064/1470 nm dual-wavelength good-bad cavity system. The synchronous cavity-length change between two dual-wavelength systems is realized by using the phase locking technique of 1064 nm goodcavity lasers. Therefore, the beating linewidth of 1470 nm badcavity lasers will also be reduced considering that the 1064/1470 nm dual-wavelength lasers share the one cavity. The tracking accuracy of 1064 nm good-cavity lasers is better than 3×10-16at 1 s after phase-locking, and the linewidth of 1470 nm bad-cavity laser is reduced to 77 Hz. The linewidth of active optical frequency standard is still limited by the light shift, collision shift and Zeeman shift. The beating signal of magnetic sublevels corresponding to the Cs 1470 nm clock transition is observed under Zeeman effect. Further research is needed, such as, the design of vacuum chamber and magnetic shielding, to reduce the linewidth of the continuous 1470 nm active optical frequency standard.
We realize the lasing of cesium active optical clock with 459 nm laser pumping, which operates deep in the optical bad-cavity regime. The ratio between cavity bandwidth and gain bandwidth is 55.08 theoretically. With 459 nm laser pumping, the population inversion occurs between the cesium 7S1/2state and 6P3/2state, and the stimulated radiation between the two states is realized. The 1469.9 nm output signal of cesium active optical clock can reach a power of 8 μW. The output power also shows a threshold character with pumping laser power and can be influenced by the Cs cell temperature. This active optical clock has an advantage in stability over the conventional optical clocks, due to its suppression of cavity pulling effect, which is also demonstrated experimentally.
Abstract Active optical clocks take advantage of the substantial suppression of cavity pulling in the bad‐cavity lasing regime and feature the simple structure and excellent portability. In the extreme case, where the cavity mirror reflection approaches zero and cannot support any quasi‐bound modes for light waves, conventional bad‐cavity lasers become the cavityless lasing and the cavity pulling vanishes. Consequently, the laser frequency is determined entirely by the atomic transition. This work is dedicated to theoretically explore the potential application of the cavityless lasing in active optical clocks. Without loss of generality, Cs atoms with well‐established quantum control techniques are employed as the gain medium that is pumped by a 459‐nm laser. The clock laser wavelength is 1470 nm. The simulation shows that the frequency stability of the clock laser with feasible physical quantities reaches at 1 s of averaging time, one order of magnitude better than the recently demonstrated compact passive optical clocks that are built upon a two‐photon transition in a hot Rb vapor and upon the modulation transfer spectroscopy of thermal Cs atoms. Such compact cavityless lasing‐based active optical clocks have the broad application prospect in satellite navigation and communications and promise an architecture for the integrated photonic metrology.
Abstract Optical clocks with thermal atoms are characterized by compact size, simple structure, reduced weight, and low power consumption and have the potential for broad out-of-the-lab and commercial applications. Here, we demonstrate a 459 nm optical clock based on the 6S 1/2 –7P 1/2 transition in thermal 133 Cs atoms. Two methods, modulation transfer spectroscopy (MTS) and frequency modulation spectroscopy (FMS), are employed to stabilize the frequency of a 459 nm commercial laser to the atomic transition. The MTS-MTS and MTS-FMS beat-note measurements show short-term frequency stabilities of 3.7 × 10 − 13 / τ and 6.4 × 10 − 13 / τ , respectively, at the averaging time τ . The 459 nm passive optical clock further serves as the pump for an active 1470 nm optical clock based on the cavityless lasing. The resultant 1470 nm output power reaches over 10 μW and the pump-beam-induced light shift is estimated to be 2 π × 11 Hz with a fractional uncertainty of 2.4 × 10 −18 . These results demonstrate the feasibility of hybridizing passive and active optical clocks, providing a promising route toward compact multi-wavelength optical frequency standards.