Weight functions for biases in atomic frequency standards.

Many perturbations that affect atomic frequency standards vary during the period of measurement. To include this time variation, we introduce 3 time-dependent weight functions built from the solution of the unperturbed equations of motion of a 2-level system. The integral of the time-dependent part of a perturbation with a weight function gives the associated first-order change in transition probability. Biases are then found easily. The same weight function may be used for different perturbations, thus unifying the derivation of their associated biases. We give several examples of the use of weight functions.

Microwave leakage-induced frequency shifts in the primary frequency standards NIST-F1 and IEN-CSF1.

In atomic fountain primary frequency standards, the atoms ideally are subjected to microwave fields resonant with the ground-state, hyperfine splitting only during the two pulses of Ramsey's separated oscillatory field measurement scheme. As a practical matter, however, stray microwave fields can be present that shift the frequency of the central Ramsey fringe and, therefore, adversely affect the accuracy of the standard. We investigate these uncontrolled stray fields here and show that the frequency errors can be measured, and indeed even the location within the standard determined by the behavior of the measured frequency with respect to microwave power in the Ramsey cavity. Experimental results that agree with the theory are presented as well.

Power dependence of the frequency bias caused by spurious components in the microwave spectrum in atomic fountains.

The presence of spurious spectral components in the microwave excitation may induce frequency shifts in an atomic fountain frequency standard. We discuss how such shifts behave as a function of power variations of the excitation carrier and in the spur-to-carrier ratio. The discussion here is limited to the case of single-sideband spurs, which are generally much more troublesome due to their ability to cause frequency shifts. We find an extremely rich and unintuitive behavior of these frequency shifts. We also discuss how pulsed operation, typical of today's fountain frequency standards, relates to frequency shifts caused by spurs in the microwave spectrum. The conclusion of these investigations is that it is, at best, difficult to use elevated power microwaves in fountain frequency standards to test for the presence of spurs in the microwave spectrum.

Power dependence of distributed cavity phase-induced frequency biases in atomic fountain frequency standards.

We discuss the implications of using high-power microwave tests in a fountain frequency standard to measure the frequency bias resulting from distributed cavity-phase shifts. We develop a theory which shows that the frequency bias from distributed cavity phase depends on the amplitude of the microwave field within the cavity. The dependence leads to the conclusion that the frequency bias associated with the distributed cavity phase is typically both misestimated and counted twice within the error budget of fountain frequency standards.