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Physical Review Letters

Giant Spin Relaxation of an Ultracold Cesium Gas

Johannes Söding, David Guéry-Odelin, Pierre Desbiolles, G. Ferrari, Jean Dalibard

Published Mar 2, 1998• 105 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.80.1869

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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{}${10}^{\mathrm{\ensuremath{-}}12}$ 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.
We present theoretical calculations of thermally averaged elastic cross sections and spin-relaxation rate coefficients in the temperature range 0.1 to $300\ensuremath{\mu}\mathrm{K}$ for magnetically trapped, doubly polarized cesium atoms. The calculations reproduce the recent experimental results of Arndt et al. (1997) and S\"oding et al. (1998) for cases where the ${a}^{3}{\ensuremath{\Sigma}}_{u}$ ground state potential of Cs2\mathrm{Cs}{}_{2}Cs2​ possesses a large scattering length ( ∣A3∣>35nm|{A}_{3}|>35\mathrm{nm}∣A3​∣>35nm) and the magnitude of the second-order spin-orbit interaction is scaled to reproduce room temperature scattering data.
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 analyze all of the cold-collision data for Cs, consisting of atomic fountain frequency shifts and elastic scattering rates, to determine phase parameters that completely characterize cold collisions between two ground-state cesium atoms. We show that the fast decays of spin-polarized gas samples in two recent attempts to reach Bose-Einstein condensation in cesium are due to potential and Feshbach resonances which enhance the depolarizing atom-atom collisions. We discuss the prospects for realizing Bose-Einstein condensation in 133Cs{}^{133}\mathrm{Cs}133Cs and in 135Cs{}^{135}\mathrm{Cs}135Cs.