Accurate Evaluation of Microwave-Leakage-Induced Frequency Shifts in Fountain Clocks

We report theoretical calculations of the transition probability errors introduced by microwave leakage in Cs fountain clocks, which will shift the clock frequency. The results show that the transition probability errors are affected by the Ramsey pulse amplitude, the relative phase between the Ramsey field and the leakage field, and the asymmetry of the leakage fields for the upward and downward passages. This effect is quite different for the leakage fields presenting below the Ramsey cavity and above the Ramsey cavity. The leakage-field-induced frequency shifts of the NIM5 fountain clock in different cases are measured. The results are consistent with the theoretical calculations, and give an accurate evaluation of the leakage-field-induced frequency shifts, as distinguished from other microwave-power-related effects for the first time.