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Collisional Studies of Ultracold Cesium

J. L. Bliss

Published Jul 25, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.7907/fcz4-pd11

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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 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 report on calculations of the elastic cross section and thermalization rate for collision between two maximally spin-polarized chromium atoms in the cold and ultracold regimes, relevant to buffer-gas and magneto-optical cooling. We calculate ab initio potential-energy curves for Cr2{\text{Cr}}_{2}Cr2​ and the van der Waals coefficient C6{C}_{6}C6​, and construct interaction potentials between two colliding Cr atoms. We explore the effect of shape resonances on the elastic cross section, and find that they dramatically affect the thermalization rate. Our calculated value for the sss-wave scattering length is compared in magnitude with a recent measurement. We propose that a dip in the elastic rate coefficient could be experimentally exploited to obtain an accurate value for the scattering length.
The use of a cryogenic apparatus has several advantages for the magneto-optical and magnetostatic trapping of atoms. We have measured the lifetimes of magneto-optical and magnetostatic traps for cesium to be greatly increased in a cryogenic vacuum environment relative to a room-temperature vacuum environment, due to reduced background pressure and reduced mass and kinetic energy of background gas atoms. Another advantage of a cryogenic apparatus is that superconducting magnetic field coils can easily be used to generate very high magnetic field gradients for stronger confinement of the trapped atoms. We report the first measurements of the stability of MOT's at high magnetic field gradients and laser intensities, and compare the results to a model based on evaporation of atoms from the MOT using a Fokker-Planck equation approach. This model is more consistent with the data than an alternative model based on ejection of atoms by magnetic dipole forces. We also measure the dynamical parameters for magneto-optically trapped atoms at both high and low magnetic field gradients and with trapping laser intensities above saturation and compare the data to a simple physical model based on polarization gradient cooling. Consistent with measurements by other groups, the measured friction is consistent with the polarization gradient model, but the measured spring constant is drastically reduced and more consistent with the predictions of the Doppler theory.
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​.
With the advent of evaporative cooling methods, atomic collisions can be studied at microkelvin and even sub-microkelvin temperatures. At these energies, resonance and threshold phenomena become very pronounced. Near zero-energy resonances lead to large variations in collision cross sections with energy. Magnetically tunable Feshbach resonances have been observed, which allow elastic collision cross sections and scattering lengths to be tuned over large ranges with small changes in an applied magnetic field. These resonance effects are extremely sensitive to small variations in atomic interaction parameters, including scattering lengths. The combined results of ultracold atomic collision and photoassociation spectroscopy experiments is leading to a complete and consistent picture of collisions of ultracold alkali 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.