Comment on ‘First accuracy evaluation of NIST-F2’

Abstract

We discuss the treatment of the systematic frequency shifts due to microwave lensing and distributed cavity phase in "First accuracy evaluation of NIST-F2" 2014 Metrologia 51 174-182. We explain that the microwave lensing frequency shift is generally non-zero and finite in the limit of no applied microwave field. This systematic error was incorrectly treated and we find that it contributes a significant frequency offset. Accounting for this shift implies that the measured microwave amplitude dependence (e.g due to microwave leakage) is comparable to the total reported inaccuracy. We also discuss the importance of vertically aligning the fountain perpendicular to the axis of the cavity feeds, when the cavity has only two independent feeds. Finally, we note that background gas collisions have a different behavior for cold clock atoms than for clock atoms at room-temperature, and therefore room temperature measurements do not directly apply to lasercooled clocks.We comment on several aspects of the recent accuracy evaluation of NIST-F2 [1], which reported a total systematic uncertainty of 1.1×10 −16 . Our most significant remark regards the evaluation of the microwave lensing frequency shift [2-6], which was briefly described in [1] and more fully presented in a recent preprint [7]. They calculated a frequency offset of 0.2×10 −16 that goes to zero in the limit of zero microwave amplitude. We show that this frequency shift of NIST-F2 is larger, of order 0.9×10 −16 , and comparable to other evaluations, which range from 0.6×10 −16 to 0.9×10 −16 [4][5][6]. In [1] Heavner et al. included microwave lensing with other systematic errors that depend on microwave amplitude, such as microwave leakage. When the shift that we calculate is removed from their measured amplitude dependence, the clock's frequency has a significant amplitude dependence with an offset at optimal amplitude from other amplitude dependent shifts (e.g. microwave leakage) that is comparable to the total systematic

Measurement of the Microwave Lensing shift in NIST-F1 and NIST-F2

“…By the time the atoms exit the Ramsey-cavity below-cutoff waveguide there are therefore no resonant microwaves being generated in the experiment. [12]. We see good agreement between all of our data and with the theory in [1] and statistically-significant disagreement with the theory in [2,12,14].…”

Systematic Effects in Atomic Fountain Clocks

“…Because atoms in a fountain are localized to less than a microwave wavelength, the resonant microwave dipole forces do not yield resolved photon recoils, but instead act as weak focusing and defocusing lenses on the atom wave packets. The resulting shift depends on the clock geometry and is typically 6×10 17 to 9×10 17 for fountains [4][5][6][7][8]17], and larger for the microgravity clock PHARAO, 11.4×10 17 [22]. There is currently some controversy since the recent NIST treatment [16,18] predicts a much smaller shift, 1.6×10 17 , disagreeing with the prior results [4][5][6][7]17].…”

“…The numerator is the perturbation of the transition probability due to lensing and the denominator is the Ramsey fringe amplitude. Both go to zero as , yielding a non-zero frequency shift in the limit of zero microwave amplitude [6,8,17], in contrast to [12,15,16]. Additionally, the NIST treatment gives zero frequency shift for all x and a/w 2 in Fig.…”

“…The resulting shift depends on the clock geometry and is typically 6×10 17 to 9×10 17 for fountains [4][5][6][7][8]17], and larger for the microgravity clock PHARAO, 11.4×10 17 [22]. There is currently some controversy since the recent NIST treatment [16,18] predicts a much smaller shift, 1.6×10 17 , disagreeing with the prior results [4][5][6][7]17]. The NIST treatment and two recent fountain accuracy evaluations have considered that the microwave lensing shift goes to zero in the limit of zero microwave amplitude [12,15,16,19].…”

“…The m=1 variations are phase gradients, which combine with fountain tilts to produce DCP shifts that are naturally large [2][3][4][5]. The m=1 gradients from the feeds usually have a large dependence on microwave amplitude and it is helpful to use this to vertically align the fountain, along a single axis with two independent feeds [3,4,17] and along two horizontal axes with four independent feeds [2,20,21]. To exclude m=1 phase gradients from resistance inhomogeneities, the tilt sensitivity of the fountain is measured for /2 pulses and nulled by adjusting the relative feed amplitudes [2,3].…”