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arXiv:1304.3486 · Physical Review Letters

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

Kurt Gibble

Published May 3, 2013• 71 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.110.180802

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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.
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 investigate decoherence in atom interferometry due to scattering from a background gas and show that the supposition that residual coherence is due to near-forward scattering is incorrect. In fact, the coherent part is completely unscattered, although it is phase shifted. This recoil-free process leaves both the atom and the gas in an unchanged state, but allows for the acquisition of a phase shift. This is essential to understanding decoherence in a separated-arm atom interferometer, where a gas of atoms forms a refractive medium for a matter wave. Our work elucidates the actual microscopic, many-body, quantum-mechanical scattering mechanism that gives rise to prior phenomenological results for the phase shift and decoherence.
We investigate decoherence in atom interferometry due to scattering from a background gas and show that the supposition that residual coherence is due to near-forward scattering is incorrect. In fact, the coherent part is completely unscattered, although it is phase shifted. This recoil-free process leaves both the atom and the gas in an unchanged state, but allows for the acquisition of a phase shift. This is essential to understanding decoherence in a separated-arm atom interferometer, where a gas of atoms forms a refractive medium for a matter wave. Our work elucidates the actual microscopic, many-body, quantum-mechanical scattering mechanism that gives rise to prior phenomenological results for the phase shift and decoherence.
We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an 27Al+^{27}\mathrm{Al}^{+}27Al+ clock to enable a total fractional systematic uncertainty below ${10}^{\ensuremath{-}18}$. For this clock, with 38(19) nPa of room-temperature H2{\mathrm{H}}_{2}H2​ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order ${10}^{\ensuremath{-}16}$ at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be $\ensuremath{-}0.6(2.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$, where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ bound used for collisional phase shift of the 27Al+^{27}\mathrm{Al}^{+}27Al+ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.
Collisions with background gas particles can shift the resonance frequencies of atoms in atomic clocks. The internal quantum states of atoms can also become entangled with their motional states due to the recoil imparted by a collision, which leads to a further shift of the clock frequency through the relativistic Doppler shift. It can be complicated to evaluate the Doppler and collisional frequency shifts for clock atoms in such entangled states, but estimates of these shifts are essential in order to improve the accuracy of optical atomic clocks. We present a formalism that describes collisions and relativistic Doppler shifts in a unified manner, and can therefore be used to accurately estimate collisional frequency shifts in trapped-atom clocks.