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Physical Review Letters

Direct Observation of s -Wave Atomic Collisions

Kurt Gibble, Seongsik Chang, Ronald Legere

Published Oct 2, 1995• 84 citations

Abstract

We observe the angular distribution of $s$-wave scattering of Cs atoms in an atomic fountain by selecting and probing atomic velocities. At an average temperature of $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.89$ $\ensuremath{\mu}$K the scattering is predominantly $s$-wave and we have a sensitivity to $p$-wave cross sections as small as 0.1% of the $s$-wave. The cross section is $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{2}$ for atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$, ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ state colliding with atoms distributed among the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$, ${m}_{F}$ states. We also demonstrate a multiply loaded magneto-optic trap and a temperature of 1.53(7) $\ensuremath{\mu}$K.

DOI: 10.1103/physrevlett.75.2666

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We observe the angular distribution of

s

-wave scattering of Cs atoms in an atomic fountain by selecting and probing atomic velocities. At an average temperature of

T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.89

\ensuremath{\mu}

K the scattering is predominantly

s

-wave and we have a sensitivity to

p

-wave cross sections as small as 0.1% of the

s

-wave. The cross section is

4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{2}

for atoms in the

F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3

,

{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

state colliding with atoms distributed among the

F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4

,

{m}_{F}

states. We also demonstrate a multiply loaded magneto-optic trap and a temperature of 1.53(7)

\ensuremath{\mu}

K.

We have measured the elastic collision cross section for spin polarized atomic cesium. Neutral cesium atoms are optically cooled, then loaded into a dc magnetic trap. We infer the scattering rate from the rate at which anisotropies in the initial energy distribution are observed to relax. The cross section for F=3,

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

=-3 on F=3,

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

=-3 is 1.5(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$

{\mathrm{cm}}^{2}

, and is independent of temperature from 30 to 250 \ensuremath{\mu}K. This determination clarifies the technical requirements for attaining Bose-Einstein condensation in a magnetically trapped Cs vapor. We also study heating due to glancing collisions with 300 K background Cs atoms.

We demonstrate a juggling atomic fountain by launching two laser-cooled balls of

{}^{133}\mathrm{Cs}

atoms in rapid succession. The atoms collide near the top of the fountain and, by varying the delay between launches, we scan the collision energy from 19 to $150\ensuremath{\mu}\mathrm{K}$. We measure the differential scattering cross section and isolate the contributions from different partial waves including their interferences. We observe the

s

-wave energy dependence and the

p

-wave scattering threshold. We infer a triplet

{}^{133}\mathrm{Cs}

-wave scattering length of ${\ensuremath{-}400a}_{0}$ and a

p

wave of $({\ensuremath{-}107a}_{0}{)}^{3}$ for

s

.

We measure the cross section for

s

-wave collisions of Cs atoms in a magnetic trap. From the relaxation of the atomic cloud towards thermal equilibrium, we infer that the cross section varies as

1/T

over the temperature range $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5--60\ensuremath{\mu}\mathrm{K}$. It takes at each measured temperature the maximum allowed value for polarized bosons. This indicates a zero-energy resonance generated by a bound or virtual state less than $5\ensuremath{\mu}\mathrm{K}$ from the dissociation threshold.

We have measured the time taken for a magnetically trapped cloud of cold cesium atoms in the ${(F=3,m}_{F}=\ensuremath{-}3)$ ground state to rethermalize from a nonequilibrium spatial and velocity distribution. From these measurements we infer the dependences of the elastic scattering cross section on temperature and magnetic field in the ranges $1\ensuremath{-}30\ensuremath{\mu}\mathrm{K}$ and 0.05--2.0 mT, respectively. We determine a lower bound on the magnitude of the $(3,\ensuremath{-}3)+(3,\ensuremath{-}3)$ s-wave scattering length of

{940a}_{0}.