Pulling by Neighbouring Transitions and its Effects on the Performance of Caesium-Beam Frequency Standards

Pulling by the wings of neighbouring field-dependent lines is usually taken into account in accuracy evaluation of caesium-beam frequency standards. Its magnitude is commonly calculated from the observed asymmetry of the neighbouring lines using a well-known formula in which the shape of all the Rabi lines is approximated with Lorentzian profiles of the same width. In this paper it is shown that use of these approximations yields in most cases grossly underestimated results for the pulling, and that the real shape of the Rabi wings must be computed in order to match experimental data. Line shapes far from Lorentzian and different widths for the different lines are obtained if the real rf field profile and the actual velocity distributions for each state are used. Unexpectedly high values are found in this way, which indicate this kind of frequency pulling as possibly the biggest single cause of inaccuracy in commercial caesium beams and a bias to be re-evaluated in primary laboratory standards. Theoretical computations show good agreement with experimental data and suggest that the well-known average frequency difference of about +1 × 10 -12 which is shown by the ensemble of all short commercial standards with respect to long primary tubes may be traced to Rabi pulling. The effect turns out to be dependent on modulation type and parameters. Dependence on rf power is also studied, which may be the primary cause of temperature sensitivity and flicker noise in short tubes, and the roles of source temperature and beam optics variations in relation to long-term drift are indicated.