Publisher's Note: Ramsey spectroscopy, matter-wave interferometry, and the microwave-lensing frequency shift [Phys. Rev. A 90 , 015601 (2014)]

The ACES/PHARAO space mission

“…The effect of the transverse phase gradient in an unperfect cavity is currently under investigation in a collaboration with K. Gibble [39,16]. Among all other small effects, the recoil shift with microwave photons or microwave lensing effect remains to be analyzed in greater depth [40]. The effect is of the order of 1·10 −16 , but the exact value depends on the initial atom's wave function size and on the geometry of the cesium tube.…”

First uncertainty evaluation of the FoCS-2 primary frequency standard

“…Several frequency shifts are due to microwave field perturbations either in the free-evolution region or in the Ramsey cavity. These contributions come from spurious spectral lines in the microwave field spectrum [39], microwave leakage [40], the distributed cavity phase shift (DCPS) [41,42], microwave lensing [43,44] and, in the case of the continuous fountain, the end-to-end phase shift [29]. In the following we discuss the microwave spectrum, microwave leakage, the end-to-end phase shift, and the DCPS.…”

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

“…Regarding the dependence on the initial wave packet size, Ashby et al [4] find "the magnitude of the effect is strongly dependent on this parameter and there are a number of equally physically reasonable choices which predict very different magnitudes." Although Jefferts et al claim that "Never in [1] or previous references [2][3][4]8], does the author ever explain what atom wave packet size he is using for his calculations of corrections as used in [2][3][4]" [1], in fact I showed in my original treatment [8] that the microwave lensing frequency shift depends on the velocity distribution of the cold atoms, but not on the initial wave packet size "because, in essence, the frequency shift from Eq. (3) is proportional to the difference of the dressed state populations, whether the dressed state populations are for one atom or the ensemble" [8].…”

“…The dipole force therefore varies importantly across the wave packet, weakly focusing and defocusing the two dressed states [2,8]. However, NIST considers that the dipole force for these atoms is everywhere 0, incorrectly yielding no lensing shift for a small initial atom cloud.…”

“…The relevance of the deBroglie wavelength is unclear since the lasercooled atoms have not thermalized. Having shown in [8] that the lensing shift is independent of the initial wave packet size allows us in [5,[9][10][11] to "semiclassically treat the atom propagation, originating from a point source and having classical trajectories with deflections" [2] given by the dipole forces. While not essential, this "semiclassical approximation, which neglects the atomic diffraction of the apertures, simplifies the calculations and yields valuable clarity" [2].…”