Abstract: Based on the principles of quantum mechanics and the locking algorithm of optical clocks, the generation mechanism of the optical clock output frequency noise is analyzed. Stabilities of single-ion optical clocks was derived from the results of Monte-Carlo simulations and compared with the experimental results. The times of the single ion interrogated by clock laser in each frequency feedback cycle N, and the gain coefficient g, were scanned respectively in simulation to studying the relationship between these parameters and the stabilities of optical clocks. Results show that the 1s stability of the optical clocks is insensitive to N and will degrade when g > 0.45. In addition, compared to the quantum projection noise, stabilities caused by the clock laser's linear drift is negligible. The proposed simulation method of single-ion optical clocks can be easily achieved and applied to evaluate the stability of optical clocks with custom parameters.

Key words: quantum optics, stability, Monte-Carlo method, optical frequency comparison