Frequency pulling in cesium beam frequency standards due to delta M=±1 (sigma) transitions

Results of a theoretical investigation of the frequency pulling by sigma transitions and some comparisons with an actual cesium dual-beam tube are presented. It is shown that the sigma transitions adjacent to the clock transition always involve one of the clock levels so their frequency pulling (Ramsey pulling) differs fundamentally from the pulling by pi transitions (Rabi pulling). Rabi pulling is caused by the residual slope due to unbalanced pi transitions and can be significantly reduced by background slope detection techniques. Ramsey pulling results from a fundamental shift in the frequency of the clock transition rather than a background slope. Ramsey pulling can only be reduced by decreasing the sigma transitions and the population asymmetries. A single-beam tube has been designed that has greatly reduced sigma transitions compared with the dual-beam tubes