Reducing cavity-pulling shift in Ramsey-operated compact clocks

We describe a method to stabilize the amplitude of the interrogating microwave field in compact atomic clocks working in a Ramsey approach. In this technique, we take advantage of the pulsed regime to use the atoms themselves as microwave amplitude discriminators. Specifically, in addition to the dependence on the microwave detuning, the atomic signal after the Ramsey interrogation acquires a dependence on the microwave pulse area (amplitude times duration) that can be exploited to implement an active stabilization of the microwave field amplitude, in a similar way in which the Ramsey clock signal is used to lock the local oscillator frequency to the atomic reference. This stabilization results in a reduced sensitivity of the clock frequency to microwave amplitude fluctuations that are transferred to the atoms through the cavity-pulling effect. The proposed technique is then effective to improve the clock stability and drift on medium and long term. We demonstrate the method for a vapor-cell clock working with a hot sample of atoms but it can be extended to cold-atom compact clocks.