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Journal of Physics B Atomic Molecular and Optical Physics

Collisions in a ballistically expanding cloud of cold atoms in an atomic fountain

Witold Chałupczak, K. Szymaniec

Published Jan 10, 2007• 8 citations
Publisher

Abstract

We have employed an intuitive model and 3D Monte Carlo simulations to study the effect of ballistic expansion of the atomic cloud on the collision energies and the resulting frequency shift in a fountain clock. In particular, we show that the energies relevant for collisions contributing to the clock shift correspond to temperatures which may be significantly smaller than the temperature of the cloud at launch. Both the assumptions and predictions of our model are related to realistic parameters of operating caesium fountain clocks.

DOI
10.1088/0953-4075/40/2/007

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We have employed an intuitive model and 3D Monte Carlo simulations to study the effect of ballistic expansion of the atomic cloud on the collision energies and the resulting frequency shift in a fountain clock. In particular, we show that the energies relevant for collisions contributing to the clock shift correspond to temperatures which may be significantly smaller than the temperature of the cloud at launch. Both the assumptions and predictions of our model are related to realistic parameters of operating caesium fountain clocks.
The number of atoms detected and the contrast of Ramsey fringe are critical operating parameters in an atomic fountain clock. To optimize these operating parameters, a Monte Carlo method is used to simulate the evolution of the atomic cloud. It is found that the physical variables, including atomic temperature, the launching direction of the atomic cloud, and the initial position of the atomic cloud, have a large influence on the ratio of the falling-back atoms to the launching atoms, and consequently on the detected atomic number, and that the atomic temperature affects the pattern of the Ramsey fringe. In the experiment, these relevant physical variables are optimized and a falling-back ratio as high as 8.6%±0.4% is obtained for a cesium atomic fountain with a launch height of 1 m. Moreover, the Ramsey fringe is experimentally optimized and the contrast of the central Ramsey fringe reaches 90%. This optimization method is also applicable to similar experiments with cold atoms.
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.
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 $2({\ensuremath{\lambda}}_{10}\ensuremath{-}{\ensuremath{\lambda}}_{20})/({\ensuremath{\lambda}}_{10}+{\ensuremath{\lambda}}_{20})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.1(6)$.