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As atomic clocks and frequency standards are increasingly operated in situations where they are exposed to environmental disturbances, it becomes more necessary to understand how variations of each clock component impact the clock output, in particular the local oscillator (LO). Most microwave atomic clocks in operation today use quartz crystal LOs with excellent short-term noise variation but large unwanted long-term drift. Fortunately, this slow drift is mitigated by repeatedly comparing the atomic reference frequency to the LO and applying corrections each iteration through a control algorithm. This article focuses on the shot-to-shot corrections themselves. To optimize clock performance, it is important to determine whether disturbances on the output are due to variations of the LO that the control loop failed to remove or variations of the reference frequency itself. Some of this can be diagnosed using the output frequency's Allan deviation (ADEV), the traditional measure of clock performance. However, the ADEV of the corrections reveals somewhat different information, specifically more direct information about all disturbances that the measurement system detects and compensates for, from the LO or elsewhere. In this article: we 1) derive the baseline shot-noise-limited noise floor for this ADEV, 2) validate and adjust for the complexities of our control loop with a computer model, and 3) examine model results and laboratory data that lie on or diverge from the noise floor to understand what divergences reveal about LO and/or clock behavior. Ultimately, we show how to use this corrections-ADEV as a diagnostic to help identify the source of disturbances and drift observed on the clock output.

Linear ion trap frequency standards are among the most stable continuously operating frequency references and clocks. Depending on the application, they have been operated with a variety of local oscillators (LOs), including quartz ultrastable oscillators, hydrogen-masers, and cryogenic sapphire oscillators. The short-, intermediate-, and long-term stability of the frequency output is a complicated function of the fundamental performances, the time dependence of environmental disturbances, the atomic interrogation algorithm, the implemented control loop, and the environmental sensitivity of the LO and the atomic system components. For applications that require moving these references out of controlled lab spaces and into less stable environments, such as fieldwork or spaceflight, a deeper understanding is needed of how disturbances at different timescales impact the various subsystems of the clock and ultimately the output stability. In this paper, we analyze which perturbations have an impact and to what degree. We also report on a computational model of a control loop, which keeps the microwave source locked to the ion resonance. This model is shown to agree with laboratory measurements of how well the feedback removes various disturbances and also with a useful analytic approach we developed for predicting these impacts.