It is well established that passive frequency standards operated in pulsed mode may suffer a degradation of their frequency stability due to the frequency (FM) noise of the Local Oscillator (LO). In continuously operated frequency standards, it has been shown that a similar degradation of the frequency stability may arise, depending on the used modulation-demodulation scheme. In this paper, we report a theoretical analysis on the possible degradations of the frequency stability of a continuous fountain due to the LO FM noise. A simple model is developed to evaluate whether or not aliasing persists. This model is based on a continuous frequency control loop of a frequency standard using a Ramsey resonator. From this model, we derive a general formula, valid for all usual modulation-demodulation schemes, for the LO frequency fluctuations due to aliasing in closed loop operation. We demonstrate that in an ideal situation and for all usual modulation waveforms, no aliasing occurs if the half-period of modulation equals the transit time of atoms in the Ramsey resonator. We also deduce that in the same conditions, square-wave phase modulation provides the strongest cancellation of the LO instabilities in closed loop operation. Finally, we show that the "Dick formula" for the specific case of the pulsed fountain can be recovered from the model by a sampling operation.
PACS. 32.80Pj -Optical cooling of atoms; trapping. PACS. 42.50Vk -Mechanical effects of light on atoms, molecules, electrons, and ions.Abstract. -Starting from a 2D magneto-optical trap where cesium atoms are permanently subjected to 3D sub-Doppler cooling and 2D magneto-optical trapping, we have produced a beam of cold atoms continuously extracted along the trap axis. The simplest extraction mechanism, presently used, is the drift velocity induced by a constant magnetic field. We have used this continuous beam of atoms to produce Ramsey fringes in a microwave cavity as a first demonstration of an atomic resonator operating continuously with laser cooled atoms. The shape of the resonance pattern allows an estimate of the axial temperature, typically 200 mK. The average velocity can be adjusted from 0.7 to 3 m/s; the trap-to-atomic-beam conversion efficiency is close to one.
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