Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Measurement of Cs-Cs elastic scattering atT=30 μK

Christopher R. Monroe, Eric Cornell, Charles A. Sackett, Christopher J. Myatt, Carl Wieman

Published Jan 25, 1993• 253 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.70.414

Related papers

Collisional Studies of Ultracold Cesium

J. L. Bliss

Spin-polarized neutral cesium atoms are confined in a magnetostatic trap in a cryogenic apparatus. The atoms are prepared in the F = 4, mF = 4 state and cooled, with rf-assisted evaporative cooling, to less than 10 microKelvin. The elastic scattering cross section is measured by disequilibrating magnetostatically trapped atoms and observing the rate of equilibration. A computer simulation is presented, the results of which are used to extract the elastic scattering cross section from the measured rates of equilibration. For cesium atoms in the F = 4, mF = 4 state, the elastic cross section is confirmed to have a resonant magnitude which varies inversely with the mean kinetic energy, implying a scattering resonance. A design for a new beam source of cold neutral atoms, based on an optical funnel with a pyramid mirror configuration, is also presented.

•Jul 25, 2025•0 citations

Measurement of elastic cross section for cold cesium collisions

S. A. Hopkins, S. C. Webster, J. Arlt +4 more

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 ${940a}_{0}.$

Physical Review A•Feb 11, 2000•39 citations

Prospects for bose condensation in a dilute vapor of heavy alkali atoms

Eric Cornell

Evaporative cooling is a proven strategy for reaching new regimes of temperature and density in magnetically trapped vapors. The technique works, however, only if the intratrap collision rate dominates the rates of undesirable processes such as spin-flip inelastic collisions and collisions with untrapped background vapor. Our measurement of the elastic scattering cross section in Cs at temperatures down to 30 {mu}K, in combination with recent theoretical calculations of the inelastic scattering rate, shows that inelastic spin-flip collisions do not pose a significant obstacle to attaining Bose condensation. We measure the elastic scattering cross section by observing the rate of thermal equilibration in a trapped sample which is initially far from thermal equilibrium. I will discuss this work and other developments relevant to attaining Bose condensation.

Bulletin of the American Physical Society•May 1, 1993•0 citations

Conditions for Bose-Einstein condensation in magnetically trapped atomic cesium

Eite Tiesinga, A. J. Moerdijk, BOUDEWIJN J. VERHAAR +1 more

We study conditions necessary for the observation of Bose-Einstein condensation in a magnetically trapped sample of atomic Cs gas. These conditions are associated with the value of the elastic scattering length, the rate of elastic scattering events, and the lifetime for decay of the density due to both magnetic dipole relaxation in two-body collisions, as well as recombination to ${\mathrm{Cs}}_{2}$ in three-body collisions. We find that, on the basis of these conditions, the prospects for observing Bose-Einstein condensation are favorable for a gas of ground-state Cs atoms in the highest state of the lowest hyperfine manifold. In all calculated elastic and inelastic two-body rates we find a pronounced resonance structure, which can be understood in terms of the interplay between the singlet-triplet interaction and the hyperfine, Zeeman, and magnetic dipole interactions. The experimental observation of these resonances may help to eliminate present uncertainties about interaction potentials.

Physical Review A•Aug 1, 1992•235 citations

Observation of Low-Field Feshbach Resonances in Collisions of Cesium Atoms

Vladan Vuletić, Andrew J. Kerman, Cheng Chin +1 more

We observe several Feshbach resonances in magnetic fields below 40 G for Cs atoms trapped in a 1D optical lattice. One resonance occurs in the lowest-energy ground state $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$, ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ which is stable against inelastic binary collisions. This opens new possibilities for Bose condensation of Cs. When the elastic collision rate far exceeds the radial vibration frequency, we enter a 2D hydrodynamic regime where the thermalization rate is independent of density and temperature. Other resonances are also observed in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$, ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}3$ state through a dramatic increase in the dipolar relaxation rate.

Physical Review Letters•Feb 15, 1999•179 citations

Giant Spin Relaxation of an Ultracold Cesium Gas

Johannes Söding, David Guéry-Odelin, Pierre Desbiolles +2 more

We have measured the rate of inelastic collisions in a cloud of doubly polarized ground-state cesium atoms ( ${F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$) confined in a magnetic trap for temperatures $T$ between 8 and $70\ensuremath{\mu}\mathrm{K}$. We find a two-body rate coefficient varying as ${T}^{\ensuremath{-}0.63}$. At 8 $\ensuremath{\mu}\mathrm{K}$ it reaches $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$ which is 3 orders of magnitude larger than predicted, ruling out a Bose-Einstein condensation of Cs in this internal state.

Physical Review Letters•Mar 2, 1998•105 citations
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, mF{\mathit{m}}_{\mathit{F}}mF​=-3 on F=3, mF{\mathit{m}}_{\mathit{F}}mF​=-3 is 1.5(4)\ifmmode\times\else\texttimes\fi{}10\ensuremath−12{10}^{\mathrm{\ensuremath{-}}12}10\ensuremath−12 cm2{\mathrm{cm}}^{2}cm2, 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.
Spin-polarized neutral cesium atoms are confined in a magnetostatic trap in a cryogenic apparatus. The atoms are prepared in the F = 4, mF = 4 state and cooled, with rf-assisted evaporative cooling, to less than 10 microKelvin. The elastic scattering cross section is measured by disequilibrating magnetostatically trapped atoms and observing the rate of equilibration. A computer simulation is presented, the results of which are used to extract the elastic scattering cross section from the measured rates of equilibration. For cesium atoms in the F = 4, mF = 4 state, the elastic cross section is confirmed to have a resonant magnitude which varies inversely with the mean kinetic energy, implying a scattering resonance. A design for a new beam source of cold neutral atoms, based on an optical funnel with a pyramid mirror configuration, is also presented.
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 940a0.{940a}_{0}.940a0​.
Evaporative cooling is a proven strategy for reaching new regimes of temperature and density in magnetically trapped vapors. The technique works, however, only if the intratrap collision rate dominates the rates of undesirable processes such as spin-flip inelastic collisions and collisions with untrapped background vapor. Our measurement of the elastic scattering cross section in Cs at temperatures down to 30 {mu}K, in combination with recent theoretical calculations of the inelastic scattering rate, shows that inelastic spin-flip collisions do not pose a significant obstacle to attaining Bose condensation. We measure the elastic scattering cross section by observing the rate of thermal equilibration in a trapped sample which is initially far from thermal equilibrium. I will discuss this work and other developments relevant to attaining Bose condensation.
We study conditions necessary for the observation of Bose-Einstein condensation in a magnetically trapped sample of atomic Cs gas. These conditions are associated with the value of the elastic scattering length, the rate of elastic scattering events, and the lifetime for decay of the density due to both magnetic dipole relaxation in two-body collisions, as well as recombination to Cs2{\mathrm{Cs}}_{2}Cs2​ in three-body collisions. We find that, on the basis of these conditions, the prospects for observing Bose-Einstein condensation are favorable for a gas of ground-state Cs atoms in the highest state of the lowest hyperfine manifold. In all calculated elastic and inelastic two-body rates we find a pronounced resonance structure, which can be understood in terms of the interplay between the singlet-triplet interaction and the hyperfine, Zeeman, and magnetic dipole interactions. The experimental observation of these resonances may help to eliminate present uncertainties about interaction potentials.
We observe several Feshbach resonances in magnetic fields below 40 G for Cs atoms trapped in a 1D optical lattice. One resonance occurs in the lowest-energy ground state F=3F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3F=3, mF=3{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3mF​=3 which is stable against inelastic binary collisions. This opens new possibilities for Bose condensation of Cs. When the elastic collision rate far exceeds the radial vibration frequency, we enter a 2D hydrodynamic regime where the thermalization rate is independent of density and temperature. Other resonances are also observed in the F=3F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3F=3, ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}3$ state through a dramatic increase in the dipolar relaxation rate.
We have measured the rate of inelastic collisions in a cloud of doubly polarized ground-state cesium atoms ( F=mF=4{F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4F=mF​=4) confined in a magnetic trap for temperatures TTT between 8 and $70\ensuremath{\mu}\mathrm{K}$. We find a two-body rate coefficient varying as ${T}^{\ensuremath{-}0.63}$. At 8 $\ensuremath{\mu}\mathrm{K}$ it reaches $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$ which is 3 orders of magnitude larger than predicted, ruling out a Bose-Einstein condensation of Cs in this internal state.