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Physical Review A

Observation of a shape resonance in the collision of two cold Rb87 atoms

H. M. J. M. Boesten, Chin‐Chun Tsai, Jamie Ryan Gardner, Daniel J. Heinzen, BOUDEWIJN J. VERHAAR

Published Jan 1, 1997• 127 citations
Publisher

Abstract

We observe a shape resonance in the scattering of two ultracold $^{87}\mathrm{Rb}$ atoms, causing the colliding atoms to form a long-living compound system inside an l=2 centrifugal barrier. Its existence follows from a photoassociation experiment in a gas sample of doubly polarized $^{87}\mathrm{Rb}$ atoms. Using it we are able to carry out direct determinations of the triplet scattering length for $^{87}\mathrm{Rb}$, relevant to Bose-Einstein condensation experiments, and of the Rb+Rb ${\mathrm{C}}_{6}$ dispersion coefficient. Consequences for the $^{85}\mathrm{Rb}$ scattering length are discussed.

DOI
10.1103/physreva.55.636

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We observe the time dependence of a cold-atom collision in a pulsed photoassociation experiment. For a ggg-wave shape resonance in the 85Rb+85Rb{}^{85}\mathrm{Rb}{+}^{85}\mathrm{Rb}85Rb+85Rb system we measure the time needed to build up the resonant state by tunneling through the centrifugal barrier. Combining this with time-independent 85Rb{}^{85}\mathrm{Rb}85Rb and 87Rb{}^{87}\mathrm{Rb}87Rb photoassociation we determine the resonance energy and find evidence for the decay of the shape resonance into inelastic channels. We also determine the 85Rb+85Rb{}^{85}\mathrm{Rb}+{}^{85}\mathrm{Rb}85Rb+85Rb and 87Rb+87Rb{}^{87}\mathrm{Rb}{+}^{87}\mathrm{Rb}87Rb+87Rb C6{C}_{6}C6​ coefficient and triplet scattering lengths without relying on ab initio calculations.
We extract information about collisions of ultra-cold ground-state rubidium atoms from observations of a g-wave shape resonance in the 85Rb + 85Rb system via time-independent and time-dependent photoassociation. The shape resonance arises from a quasi-bound state inside a centrifugal barrier that enhances the excitation to the bound electronically excited state by the photoassociation laser in the time-independent experiment. The shape resonance is sufficiently long-lived that its build-up through the barrier can be observed by first depleting it via a photoassociation laser pulse and then measuring the rate of photoassociation by a second laser pulse with a variable delay time. A combined method of analysis of the time-independent and time-dependent experiments is presented. We discuss the spectroscopy of states of two particles with spin trapped inside a centrifugal barrier, interacting via direct and indirect spin-spin interactions.
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We study the collisions of doubly spin-polarized 85Rb{}^{85}\mathrm{Rb}85Rb atoms at millikelvin temperatures using photoassociation spectroscopy. Because the atoms are spin polarized, only triplet collisional states are formed. This leads to photoassociation spectra of a particularly simple form, which provide a very direct probe of the ground state collision. These spectra are analyzed to yield the ground state triplet scattering length ${\ensuremath{-}1000a}_{0}<{a}_{T}<{\ensuremath{-}60a}_{0}$ for 85Rb{}^{85}\mathrm{Rb}85Rb, +85a0<aT<+140a0{+85a}_{0}<{a}_{T}<{+140a}_{0}+85a0​<aT​<+140a0​ for 87Rb{}^{87}\mathrm{Rb}87Rb, and the product of the DDD-line dipole matrix elements $d({P}_{1/2})d({P}_{3/2})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8.75\ifmmode\pm\else\textpm\fi{}0.25$ a.u.
The presence of shape resonances due to tunneling through the centrifugal barrier modifies strongly the dynamics of cold atom scattering. As shown on the example of the ground and lowest triplet electronic states of the 85Rb^{85}\mathrm{Rb}85Rb133Cs^{133}\mathrm{Cs}133Cs molecule, the crucial parameter is, as usual for cold collisions, the scattering length. A general description of shape resonances of diatomic molecules is given from three simple single channel asymptotic models, whose respective performances are discussed. The first model, which consists of a ${R}^{\ensuremath{-}6}$ potential limited at short range by a repulsive wall, positioned to reproduce the sss-wave scattering length, accounts satisfactorily for the main system-independent properties of shape resonances. Introduction in the model of energy- and angular-momentum-dependent nodal lines specific to the inner part of the potential greatly improves its efficiency. When the energy and angular momentum dependence of the nodal lines cannot be deduced from full potential calculations or from experiment, a rough, but universal, estimate of these properties is obtained by extending the ${R}^{\ensuremath{-}6}$ behavior of the potential up to the origin.
We report the first observation of the highest lying bound levels of the ground electronic state of ^85Rb2 by means of optical double resonance (free-bound-bound) photoassociation spectroscopy of colliding, laser-cooled ^85Rb atoms. Twelve levels with binding energies from 0.13 to 20 Ghz are observed. We carry out an inverse perturbation analysis of these levels that takes full account of the hyperfine-induced singlet-triplet mixing with a coupled channels approach. This analysis yields previously undetermined atomic interaction parameters that are crucial for the understanding of Rb ultracold collisions and Bose-Einstein condensates. Complete consistency is obtained with all previously measured cold collision properties of Rb. We gratefully acknowledge the support at Texas of the R. A. Welch Foundation, the NSF, and the Microgravity Science and Applications Division of NASA.