Frequency shift analysis tools for high performance optically pumped cesium beam frequency standard

We have implemented a digital servo system on an optically pumped cesium beam frequency standard. It controls three parameters: the frequency of the Ultra Stable Oscillator, the microwave power of the signal which interrogates the cesium atoms and the static magnetic field in the cavity. The short tube developed at LHA has been evaluated. It shows a very satisfactory level of short and medium term frequency stability. The frequency offset (-4.10^-12) results mainly from the residual phase difference of the oscillatory field between the two interaction regions which is due to imperfections in the cavity symmetry. We describe means for evaluating the spurious frequency offset, through theoretical and experimental considerations. Assuming a square wave frequency modulation, a numerical simulation of the beam tube response is performed as a function of the microwave field amplitude, for different values of the residual phase difference ΔΦ and including the cavity pulling effect. Compared with the measurement frequency offset, the numerical simulation leads to a second order Doppler shift equal to -3.5 mHz and a residual phase difference, ΔΦ of +150 μrad. An experimental method of measurement of ΔΦ without beam reversal is used. We obtain ΔΦ=+155 μrad ±17 μrad. Finally, the clock accuracy is determined. It is equal to 4.10^-13