Effects of Servo Loop Modulation in Atomic Beam Frequency Standards Employing a Ramsey Cavity

Some kind of modulation needs to be imposed on the mi- crowave signal to acquire lock in all passive atomic frequency stan- dards. In this way a frequency-discriminating dc signal is obtained by synchronous detection, which allows control of a slave oscillator. Fre- quency stability and frequency biases of the latter under closed-loop operation depend on the type and characteristics of the used modula- tion. The case of atomic beam standards using a Ramsey cavity is stud- ied, and different modulation schemes are considered under the aspects of efficiency (obtainable stability) and insensitivity to systematic effects. Theoretical results for the dependence of these on modulation type and parameters and on microwave power are reported and discussed. schemes and their sensitivity to some systematic effects are given as a function of modulation type and parame- ters, and are calculated numerically for an existing atomic beam tube. In particular, the effects of sine-wave modu- lation and slow square-wave frequency modulation on short-term stability and on various biases are discussed. A perfect realization of these ideal schemes will be as- sumed, and system imperfections like second harmonic distortion will be overlooked in the scope of this paper. 11. SYSTEM ANALYSIS Whatever the particular coherent detection system may be, signal processing of the modulated output Pod from the atomic resonator can be ideally divided in two steps: a filter section with a time-dependent output IF synchron- ous with the modulation, and a __ phase-sensitive detector with a time-independent output Pd.