PROPERTIES OF AN OSCILLATOR SLAVED TO A PERIODICALLY INTERROGATED ATOMIC RESONATOR

In advanced atomic resonators, such as those using a fountain of cold cesium atoms or an ensemble of stored ions, the atomic medium is inter rogated periodically, and the control signal of the slaved oscillator is updated at equally spaced time intervals. We analyze the properties of the output frequency of these frequency standards. We establish th e equations that describe the time behavior of this frequency. We give the stability condition and the transient response of the frequency f eedback loop, the response to systematic frequency changes of the free running oscillator, the frequency stability for given free-running os cillator noise and given optical detection noise, and the limitation o f the frequency stability by down-conversion of the intrinsic oscillat or frequency noise (Dick effect). We point out that a second integrati on in the feedback loop may not improve significantly the rejection of slow perturbations, unless a condition relative to the timing of the atom-field interaction is verified.