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

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.