Comment on ‘Evaluation of the primary frequency standard NPL-CsF1’∗

A recent evaluation of the accuracy of the National Physical Laboratory (NPL) primary frequency standard NPL-CsF1 by K Szymaniec et al (2005 Metrologia 42 49–57) reported an overall frequency uncertainty of δν/ν0 = 1 × 10−15. This stated uncertainty includes a correction of a frequency bias of δν/ν0 = 8 × 10−16 ± 3 × 10−16 attributed by the authors to microwave leakage. We believe that the stated cause of the frequency bias, its magnitude and its stated uncertainty are in error. In their paper [1] on page 55, section 3.4 the authors state that a frequency shift in the National Physical Laboratory (NPL)CsF1 primary frequency standard induced by microwave leakage is linearly dependent on microwave power. However, several studies and models have demonstrated that the magnitude of the frequency shift caused by microwave leakage is a power series in the microwave field with a leading term linear in the field [2–4]. The frequency shift due to microwave leakage at a Ramsey excitation of, for example, 11π/2 would have a magnitude approximately 11 times the magnitude of the shift at π/2 rather than the factor of 112 = 121 assumed in [1]. The paper reporting the evaluation of NPL-CsF1 [1] did not include detailed data on the measured frequency shift as a function of microwave power. However, an earlier paper about NPL-CsF1 [5] included data which appear to be consistent with a quasi-linear relationship between frequency shift and microwave power. The data from [5] are reproduced in figure 1. Both the reported frequency bias and associated uncertainty assigned to microwave leakage in [5] are identical to those reported in the formal evaluation of NPL-CsF1 [1]. The data in figure 1 are used to support the claimed strictly linear dependence of frequency shift on microwave power. We question this claim for several reasons. First, the uncertainty bars on the data in figure 1 average more than δν/ν = 10−14, some 30 times the claimed accuracy of the corrected frequency bias. These data are too crude, in and of themselves, to justify a correction of a primary frequency standard at the δν/ν ≈ 3 × 10−16 level based on an assumed strict linearity ∗ Contribution of the US government, not subject to US copyright. between microwave power and frequency shift. Second, the data in figure 1 can also be fitted with terms proportional to the microwave field amplitude (as suggested by theory), in addition to the term assumed to be linear in the microwave power. If these terms proportional to the field are included, the frequency bias at normal power would be shifted by δν/ν ≈ 3.5×10−15, more than ten times the claimed uncertainty of the bias and more than three times the total claimed uncertainty of the standard. We note that in all previous reports of frequency bias caused by microwave leakage in fountain frequency standards, measurements of the sort shown in figure 1 have always been null-shift measurements; that is, they are used to evaluate the uncertainty of an uncorrected bias, not to make a correction for a bias. This is because microwave leakage is often unstable in time and corrections are thus difficult at best. The authors at NPL state they have based their approach on a non-resonant AC Stark shift theory [6] and invoke the paper by Boussert et al [3] as justification. The frequency shift assigned is thus given as