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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Scattering of cold atom coherences by hot atoms: Background gas collision shifts of primary fountain clocks

Kurt Gibble

Published Jul 1, 2013• 2 citations
Publisher

Abstract

We theoretically analyze frequency shifts of cold-atom clocks due to background gas collisions. Because nearly all collisions with room-temperature background gases that transfer momentum eject cold atoms from a clock, the frequency shifts for cold atoms are significantly different than those of room-temperature clocks. From general arguments, measurements of the loss of Ramsey fringe amplitude can usefully bound this source of systematic error.

DOI
10.1109/eftf-ifc.2013.6702259

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Scattering of Cold-Atom Coherences by Hot Atoms: Frequency Shifts from Background-Gas Collisions

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Frequency shifts from background-gas collisions currently contribute significantly to the inaccuracy of atomic clocks. Because nearly all collisions with room-temperature background gases that transfer momentum eject the cold atoms from the clock, the interference between the scattered and unscattered waves in the forward direction dominates these frequency shifts. We show they are ≈ 10 times smaller than in room-temperature clocks and that van der Waals interactions produce the cold-atom background-gas shift. General considerations allow the loss of the Ramsey fringe amplitude to bound this frequency shift.

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A technique to cancel the frequency shift due to cold collisions of laser-cooled atoms is proposed. Results for future clocks based on $^{135}\mathrm{Cs}$ and $^{137}\mathrm{Cs}$ are presented. We find a $^{137}\mathrm{Cs}$ fountain clock can be operated with no cold-collision shift by adjusting the population ratios in the fountain, and it may also be possible for $^{135}\mathrm{Cs}$. This technique can also be applied to other phase-sensitive measurements using cold atoms, including atom interferometers.

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Summary form only given. As the performance of optical atomic clocks improves steadily, new sources of systematic errors need to be evaluated with increasingly higher accuracy. At present, the collisional frequency shift (CFS), due to interactions with background gas atoms in the environment of the clock ions, is in some cases the next-to-leading source of systematic uncertainty for trapped-ion optical clocks. Existing approaches towards evaluating the CFS have either assumed that only glancing-angle collisions are relevant, or assumed a worst-case scenario for the phase shift imparted to clock state superposition by a collision. The former approach, which was developed for laser-cooled cesium clocks, is not applicable to the deeply trapped atomic ions used in optical clocks, while the latter approach is likely to significantly overestimate the CFS. To address this problem we have developed a framework, based on a non-perturbative quantum channel description of the collision process. Our method leads to a convenient master equation and a compact expression for the CFS. In particular, this framework can be used to estimate the CFS in situations involving many partial waves and large collisional phase shifts, which is the case with thermal background gas atoms scattering off a clock ion. Our method lends itself to practical evaluations of the CFS, by using readily calculated molecular potential curves for the ion-background gas system to extract the collisional phase shifts which lead to the CFS. As an application of this method to a realistic and relevant situation, we have numerically estimated the frequency shift of the 674 nm clock transition in Sr+due to collisions with background helium gas. We find that the CFS is much smaller than the worst-case estimate. In this talk, we describe the theoretical background and motivate the steps that lead to our framework for calculating the CFS. Following this, we present our calculations for the Sr+-He system as an example of the general method, and discuss possible extensions and improvements that will allow us to evaluate the CFS for the Sr+clock at the National Research Council Canada.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Jul 1, 2017•1 citation

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We measure a cold collision frequency shift in an ${}^{87}\mathrm{Rb}$ fountain clock that is fractionally 30 times smaller than that for Cs. The shift is $\ensuremath{-}0.38(8)\mathrm{mHz}$ for a density of $1.0(6)\ifmmode\times\else\texttimes\fi{}{10}^{9}{\mathrm{cm}}^{\ensuremath{-}3}$. We study the cavity pulling of the atomic transition and use it to cancel the cold collision shift. We also measure the partial frequency shifts of each clock state finding $2({\ensuremath{\lambda}}_{10}\ensuremath{-}{\ensuremath{\lambda}}_{20})/({\ensuremath{\lambda}}_{10}+{\ensuremath{\lambda}}_{20})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.1(6)$.

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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Apr 1, 2019•5 citations
We theoretically analyze frequency shifts of cold-atom clocks due to background gas collisions. Because nearly all collisions with room-temperature background gases that transfer momentum eject cold atoms from a clock, the frequency shifts for cold atoms are significantly different than those of room-temperature clocks. From general arguments, measurements of the loss of Ramsey fringe amplitude can usefully bound this source of systematic error.
Frequency shifts from background-gas collisions currently contribute significantly to the inaccuracy of atomic clocks. Because nearly all collisions with room-temperature background gases that transfer momentum eject the cold atoms from the clock, the interference between the scattered and unscattered waves in the forward direction dominates these frequency shifts. We show they are ≈ 10 times smaller than in room-temperature clocks and that van der Waals interactions produce the cold-atom background-gas shift. General considerations allow the loss of the Ramsey fringe amplitude to bound this frequency shift.
A technique to cancel the frequency shift due to cold collisions of laser-cooled atoms is proposed. Results for future clocks based on 135Cs^{135}\mathrm{Cs}135Cs and 137Cs^{137}\mathrm{Cs}137Cs are presented. We find a 137Cs^{137}\mathrm{Cs}137Cs fountain clock can be operated with no cold-collision shift by adjusting the population ratios in the fountain, and it may also be possible for 135Cs^{135}\mathrm{Cs}135Cs. This technique can also be applied to other phase-sensitive measurements using cold atoms, including atom interferometers.
Summary form only given. As the performance of optical atomic clocks improves steadily, new sources of systematic errors need to be evaluated with increasingly higher accuracy. At present, the collisional frequency shift (CFS), due to interactions with background gas atoms in the environment of the clock ions, is in some cases the next-to-leading source of systematic uncertainty for trapped-ion optical clocks. Existing approaches towards evaluating the CFS have either assumed that only glancing-angle collisions are relevant, or assumed a worst-case scenario for the phase shift imparted to clock state superposition by a collision. The former approach, which was developed for laser-cooled cesium clocks, is not applicable to the deeply trapped atomic ions used in optical clocks, while the latter approach is likely to significantly overestimate the CFS. To address this problem we have developed a framework, based on a non-perturbative quantum channel description of the collision process. Our method leads to a convenient master equation and a compact expression for the CFS. In particular, this framework can be used to estimate the CFS in situations involving many partial waves and large collisional phase shifts, which is the case with thermal background gas atoms scattering off a clock ion. Our method lends itself to practical evaluations of the CFS, by using readily calculated molecular potential curves for the ion-background gas system to extract the collisional phase shifts which lead to the CFS. As an application of this method to a realistic and relevant situation, we have numerically estimated the frequency shift of the 674 nm clock transition in Sr+due to collisions with background helium gas. We find that the CFS is much smaller than the worst-case estimate. In this talk, we describe the theoretical background and motivate the steps that lead to our framework for calculating the CFS. Following this, we present our calculations for the Sr+-He system as an example of the general method, and discuss possible extensions and improvements that will allow us to evaluate the CFS for the Sr+clock at the National Research Council Canada.
We measure a cold collision frequency shift in an 87Rb{}^{87}\mathrm{Rb}87Rb fountain clock that is fractionally 30 times smaller than that for Cs. The shift is $\ensuremath{-}0.38(8)\mathrm{mHz}$ for a density of $1.0(6)\ifmmode\times\else\texttimes\fi{}{10}^{9}{\mathrm{cm}}^{\ensuremath{-}3}$. We study the cavity pulling of the atomic transition and use it to cancel the cold collision shift. We also measure the partial frequency shifts of each clock state finding $2({\ensuremath{\lambda}}_{10}\ensuremath{-}{\ensuremath{\lambda}}_{20})/({\ensuremath{\lambda}}_{10}+{\ensuremath{\lambda}}_{20})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.1(6)$.