On the length of the drift region in the Ramsey cavity

The interaction of atoms in a beam with the microwave field in a separated field geometry such as a Ramsey cavity is generally described in terms of the three regions traversed successively by the atoms, namely two interaction regions of length (l) separated by a drift, or free precession, region of length L. For a monokinetic beam of velocity v, the linewidth of the central fringe in the Ramsey resonance pattern is usually expressed as delta omega equals pi v/L. A more detailed calculation shows, however, that the linewidth is equal to pi v/L asterisk, where the equivalent drift L asterisk is larger than L by an amount of the order of l/L. The correction depends on the field distribution in the interaction regions. Its origin lies in the fact that atomic precession is not limited to the field-free regions but also occurs in the interaction regions, where atomic coherence builds up or decreases continuously. Although the correction to the equivalent length of the drift region is small, it may be relevant to the evaluation of the second-order Doppler effect bias in primary cesium-beam standards to the extent that the atomic velocity is deduced from the lineshape and from the geometrical parameters of the cavity. It is shown that in current and projected standards with atoms of average thermal velocity, use of corrected dimensions may lead to a change of the calculated bias of the order of 10(exp -14), which is significant at the levels of accuracy considered nowadays.