Analysis tools for the accurate evaluation of a small frequency standard

The short, optically pumped cesium beam tube developed at Laboratoire de l'Horloge Atomique has been carefully evaluated. For that purpose, we have developed a digital servo system that controls three parameters: the frequency of the ultra stable oscillator (USO), the microwave power of the signal experienced by the cesium atoms, and the static magnetic field applied to the atoms. The frequency standard shows a very satisfactory level of short- and medium-term frequency stabilities. A relative frequency offset, measured to be 4.10(-12 ), results mainly from the residual phase difference between the oscillatory fields in the two interaction regions, which is due to imperfection in cavity symmetry. We present two different means of analyzing the causes of this spurious frequency offset using theoretical and experimental considerations. First, 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 DeltaPhi. Results include the cavity-pulling effect. Compared with the measured frequency offset, the numerical simulation leads to a second-order Doppler shift of -3.3 mHz and a residual phase difference, DeltaPhi, between the fields interacting with the atoms in the second and first regions of the Ramsey cavity, amounting to +150 murad. Second, an experimental method of measurement of DeltaPhi without beam reversal is implemented. The latter yields DeltaPhi=155+/-17 murad. Finally, the clock accuracy is determined. It is equal to +/-14.10(-13).