Evaluation of the frequency instability limited by Dick effect in the microwave ¹⁹⁹Hg⁺ trapped-ion clock

In the microwave ¹⁹⁹Hg⁺ trapped-ion clock, the frequency instability degradation caused by the Dick effect is unavoidable because of the periodical interrogating field. In this paper, the general expression of the sensitivity function g(t) to the frequency fluctuation of the interrogating field with Nπ-pulse (N is odd) is derived. According to the measured phase noise of the 40.5-GHz microwave synthesizer, the Dick-effect limited Allan deviation of our ¹⁹⁹Hg⁺ trapped-ion clock is worked out. The results indicate that the limited Allan deviations are about 1.75×10^-13/√τ and 3.03×10^-13/√τ respectively in the linear ion trap and in the two-segment extended linear ion trap under our present experimental parameters.