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Bulletin of the American Physical Society

Frequency shifts due to ultra-cold atom collisions

Kurt Gibble

Published Dec 1, 1993• 0 citations

Abstract

It was anticipated that laser cooling of atoms to 2 {mu}K would improve the accuracy and resolution of laser and microwave spectroscopies by 2 to 3 orders of magnitude. In state-of-the-art room temperature Cs frequency standards, the 9 GHz ground state hyperfine transition is measured with a fractional accuracy of 3 x 10{sup {minus}14}. Since all of the formerly known systematic effects that limit the accuracy increase either linearly or as some high power of the atom`s velocity, the accuracy of a laser cooled Cs standard should be {approx} 10{sup {minus}16}. However, at {mu}K temperatures, the de Broglie wavelengths of the atoms are much larger than the scale of the interatomic potential so that collision cross sections can be as large as {lambda}{sub dB}{sup 2}/2{pi} {approx} 10{sup {minus}10} cm{sup 2}. Here, collisional frequency shifts in a laser-cooled Cs fountain are measured to be {minus}1.4 x 10{sup {minus}12} corresponding to a cross section of 0.5 x 10{sup {minus}10} cm{sup 2}. The author also expects to report experimental results showing a potentially strong magnetic field dependence of these cross sections for fields smaller than 0.2 G. The field of ultra-cold collisions will also be reviewed.

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The spin-exchange frequency shift due to cold collisions between ground-state atoms appears to be the systematic effect which could limit the accuracy of a laser-cooled cesium fountain operating as a frequency standard. We have investigated this shift for atoms distributed among all the Zeeman substates of either the F = 4 or F = 3 hyperfine level of the 6 S 1/2 ground state of cesium and for the case where most of the atoms are prepared in F = 3, M F = 0 sublevel. The measured relative frequency shifts are respectively − 1.0·10 −21 , − 0.6·10 −21 and − 2.0·10 −21 (at/cm 3 ) −1 . These results agree with the measurements performed by Gibble and Chu at higher atom densities with atoms prepared in F = 3, M F = 0 sublevel. However, the precision of our frequency measurements is much better and is only limited at 2·10 −15 by the H-maser used as a reference oscillator. Finally, we show that the relative frequency shift due to cold collisions can be reduced to 10 −15 , while preserving a short-term frequency stability of about 10 −13 τ −1/2 .

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We demonstate a laser-cooled Cs fountain which can be used as a frequency standard. The fountain has been used to measure the frequency shift due to ultracold Cs-Cs collisions at temperatures below 2.8 \ensuremath{\mu}K. The measured shift is -12.9\ifmmode\pm\else\textpm\fi{}0.7 mHz for a density of (2.7\ifmmode\pm\else\textpm\fi{}1.5)\ifmmode\times\else\texttimes\fi{}${10}^{9}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ beginning with an even distribution (\ifmmode\pm\else\textpm\fi{}10%) among the F=3, ${\mathit{m}}_{\mathit{F}}$ states. For a fountain with 95% of the atoms in the ${\mathit{m}}_{\mathit{F}}$=0 states, we measure a frequency shift of -5.5\ifmmode\pm\else\textpm\fi{}0.5 mHz at a density of (3.5\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.

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AIP conference proceedings•Jan 1, 2005•1 citation

It was anticipated that laser cooling of atoms to 2 {mu}K would improve the accuracy and resolution of laser and microwave spectroscopies by 2 to 3 orders of magnitude. In state-of-the-art room temperature Cs frequency standards, the 9 GHz ground state hyperfine transition is measured with a fractional accuracy of 3 x 10{sup {minus}14}. Since all of the formerly known systematic effects that limit the accuracy increase either linearly or as some high power of the atom`s velocity, the accuracy of a laser cooled Cs standard should be {approx} 10{sup {minus}16}. However, at {mu}K temperatures, the de Broglie wavelengths of the atoms are much larger than the scale of the interatomic potential so that collision cross sections can be as large as {lambda}{sub dB}{sup 2}/2{pi} {approx} 10{sup {minus}10} cm{sup 2}. Here, collisional frequency shifts in a laser-cooled Cs fountain are measured to be {minus}1.4 x 10{sup {minus}12} corresponding to a cross section of 0.5 x 10{sup {minus}10} cm{sup 2}. The author also expects to report experimental results showing a potentially strong magnetic field dependence of these cross sections for fields smaller than 0.2 G. The field of ultra-cold collisions will also be reviewed.

The spin-exchange frequency shift due to cold collisions between ground-state atoms appears to be the systematic effect which could limit the accuracy of a laser-cooled cesium fountain operating as a frequency standard. We have investigated this shift for atoms distributed among all the Zeeman substates of either the F = 4 or F = 3 hyperfine level of the 6 S 1/2 ground state of cesium and for the case where most of the atoms are prepared in F = 3, M F = 0 sublevel. The measured relative frequency shifts are respectively − 1.0·10 −21 , − 0.6·10 −21 and − 2.0·10 −21 (at/cm 3 ) −1 . These results agree with the measurements performed by Gibble and Chu at higher atom densities with atoms prepared in F = 3, M F = 0 sublevel. However, the precision of our frequency measurements is much better and is only limited at 2·10 −15 by the H-maser used as a reference oscillator. Finally, we show that the relative frequency shift due to cold collisions can be reduced to 10 −15 , while preserving a short-term frequency stability of about 10 −13 τ −1/2 .

In our Cs atomic fountain, we laser cooled and trapped 10(exp 10) Cs atoms in 0.4 s. By shifting the frequencies of the laser beams, the atoms were launched upwards at 2.5 m/s and a fraction of the atoms were optically pumped into the F=3 ground state. The unwanted atoms in the F=4 ground state were removed from the fountain with radiation pressure from a laser beam tuned to excite only those atoms. The Cs atoms in the F=3 state traveled ballistically upwards, were excited by the microwave cavity, and then returned back through the same cavity in the atomic fountain configuration.

We demonstate a laser-cooled Cs fountain which can be used as a frequency standard. The fountain has been used to measure the frequency shift due to ultracold Cs-Cs collisions at temperatures below 2.8 \ensuremath{\mu}K. The measured shift is -12.9\ifmmode\pm\else\textpm\fi{}0.7 mHz for a density of (2.7\ifmmode\pm\else\textpm\fi{}1.5)\ifmmode\times\else\texttimes\fi{}

{10}^{9}

${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ beginning with an even distribution (\ifmmode\pm\else\textpm\fi{}10%) among the F=3,

{\mathit{m}}_{\mathit{F}}

states. For a fountain with 95% of the atoms in the

{\mathit{m}}_{\mathit{F}}

=0 states, we measure a frequency shift of -5.5\ifmmode\pm\else\textpm\fi{}0.5 mHz at a density of (3.5\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}

{10}^{8}

${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.

This paper describes the work performed at BNM‐SYRTE (Observatoire de Paris) over the past few years toward the improvement and the use of microwave frequency standards using laser‐cooled atoms. First, recent improvements of the 133Cs and 87Rb atomic fountains are described. An important advance is the achievement of a fractional frequency instability of 1.6 × 10−14τ−1/2 where τ is the measurement time in seconds, thanks to the routine use of a cryogenic sapphire oscillator as an ultra‐stable local frequency reference. The second advance is a powerful method to control the frequency shift due to cold collisions. These two advances lead to a frequency stability of 2 × 10−16 at 50 000 s for the first time for primary standards. In addition, these clocks realize the SI second with an accuracy of 7 × 10−16, one order of magnitude below that of uncooled devices.