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Physical Review Letters

Cancellation of the Collisional Frequency Shift in Caesium Fountain Clocks

K. Szymaniec, Witold Chałupczak, Eite Tiesinga, Carl J. Williams, S. Weyers, R. Wynands

Published Apr 13, 2007• 69 citations
Publisher

Abstract

We have observed that the collisional frequency shift in primary caesium fountain clocks varies with the clock state population composition and, in particular, is zero for a given fraction of the |F=4,mF=0) atoms, depending on the initial cloud parameters. We present a theoretical model explaining our observations. The possibility of the collisional shift cancellation implies an improvement in the performance of caesium fountain standards and a simplification in their operation.

DOI
10.1103/physrevlett.98.153002

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APS•Apr 1, 1997•0 citations
We have observed that the collisional frequency shift in primary caesium fountain clocks varies with the clock state population composition and, in particular, is zero for a given fraction of the |F=4,mF=0) atoms, depending on the initial cloud parameters. We present a theoretical model explaining our observations. The possibility of the collisional shift cancellation implies an improvement in the performance of caesium fountain standards and a simplification in their operation.
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.
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 $2({\ensuremath{\lambda}}_{10}\ensuremath{-}{\ensuremath{\lambda}}_{20})/({\ensuremath{\lambda}}_{10}+{\ensuremath{\lambda}}_{20})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.1(6)$.
Typically, primary fountain frequency standards are tested at elevated microwave powers in order to check for potential frequency shifts due to, e.g., microwave leakage or cavity phase gradients. Usually such tests are performed at nπ/2 microwave pulse area (n an odd integer), where the microwave power is set to these values typically by maximizing the contrast of the central Ramsey fringe. We have experimentally demonstrated that in this case for different n a varying clock state composition after the first Ramsey interaction can be obtained, if the average microwave power seen by the expanding atom cloud is different during the first and the second transition through the Ramsey cavity. In the presence of a clock state composition dependent collisional shift, this effect gives rise to different collisional shifts for operation at different nπ/2 pulse area.
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 have implemented a technique of optical pumping (OP) to increase the clock state populations in a caesium fountain frequency standard. Our initial experiments have demonstrated accumulation of 75% of the atoms in the mF= 0 sublevel (clock state), which can be compared to a typical 11% population of this sublevel with no additional OP applied. As the (OP) process requires scattering of some 20 photons per atom, the atomic cloud is heated by nearly 1 μK and the final number of atoms reaching the detector is reduced by up to a factor of two, depending on the molasses temperature. Using the OP technique in the NPL-CsF2 fountain we have observed a four-fold net increase of the clock state population.
A few years ago atomic fountains using cold ^133Cs atoms led to a breakthrough in the field of atomic frequency standards(A. Clairon, C. Salomon, S. Guellati, and W. D. Phillips, Europhys. Lett. 16), 165 (1991); K. Gibble and S. Chu, Phys. Rev. Lett. 70, 1771 (1993).. It was soon found that the frequency shifts induced by collisions between atoms during their fountain orbit stand in the way to drawing the full benefits from this development. A possible way out is to switch to another atomic species(K. Gibble and B.J. Verhaar, Phys. Rev. A 52), 3370 (1995).. Recent experiments have made it possible to determine cold collision parameters for pairs of rubidium atoms with unprecedented accuracy(J.M. Vogels, C.C. Tsai, R.S. Freeland, S.J.J.M.F. Kokkelmans, B.J. Verhaar, and D.J. Heinzen (submitted).). Making use of these parameters we predict the collisional frequency shifts for a ^87Rb and a ^85Rb laser-cooled clock. Our results show the prospects for new atomic clocks based on ultracold rubidium to be promising.