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 de veloped a digital servo system that controls three parameters: the frequenc y of the ultra stable oscillator (USO), the microwave power of the signal e xperienced by the cesium atoms, and the static magnetic field applied to th e atoms. The frequency standard shows a very satisfactory level of short- a nd medium-term frequency stabilities. A relative frequency offset, measured to be -4.10(-12), results mainly from the residual phase difference betwee n the oscillatory fields in the two interaction regions, which is due to im perfection in cavity symmetry. We present two different means of analyzing the causes of this spurious fre quency offset using theoretical and experimental considerations. First, a n umerical simulation of the beam tube response is performed as a function of the microwave field amplitude for different values of the residual phase d ifference Delta Phi. Results include the cavity-pulling effect. Compared wi th the measured frequency offset, the numerical simulation leads to a secon d-order Doppler shift of -3.3 mHz and a residual phase difference, Delta Ph i, between the fields interacting with the atoms in the second and first re gions of the Ramsey cavity, amounting to +150 mu rad. Second, an experiment al method of measurement of Delta Phi without beam reversal is implemented. The latter yields Delta Phi = 155 +/- 17 mu rad. Finally, the clock accuracy is determined. It is equal to +/-4.10(-13).