Comment on ``Ramsey spectroscopy, matter-wave interferometry, and the microwave-lensing frequency shift''

Abstract

Determination of the second in the International System of Units (SI) and realization of international atomic time (TAI) are among the most precise measurements of any kind and have some of the greatest impacts on technology and research, largely because the careful physical measurements are complemented by well-established and tested theories. Reference [1] describes the theory of a frequency shift from which the author calculates “corrections” to various primary frequency standards: the laser-cooled atomic microwave fountain clocks that are used to determine TAI and the SI second. According to Ref. [1], the magnitude of this frequency shift (δf/f )i s on the order of the current frequency uncertainty of the best primary frequency standards df/f ∼ 1 × 10 −16 . Corrections for this shift (microwave lensing) are currently applied to some (but not all) of the primary frequency standards that help determine TAI and the SI second [2–4]. The frequency shift described in Ref. [1], thus introduces a significant bias in TAI compared to TAI realized without the proposed shift applied. Our group has performed independent theoretical investigations into the theory of a microwave frequency shift from lensing [5], and our theory shows significantly different results than those claimed in Ref. [1]. The effect described in Ref. [1] is the result of “clipping” of the atomic wave function by limiting apertures in a primary frequency standard (PFS). It is postulated that differential clipping of the two dressed states of the atomic wave function occurs as a result of a very small transverse force on the atoms caused by a gradient in the microwave field during microwave interrogation. This small transverse force generates a displacement between the wave functions of the two dressed states on the order of a few nanometers, which is much less