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Journal of Physics B Atomic Molecular and Optical Physics

Ultracold scattering of Rb atoms and bound states of Rb2

S. Geltman

Published Oct 27, 2006• 4 citations
Publisher

Abstract

The most accurate theoretical potentials available for the interaction of a pair of ground-state Rb atoms are used to evaluate their ultracold scattering properties. The close relation between the zero-energy scattering phase shifts and the number of bound states in the potential, by Levinson's theorem, is used to assign absolute values to the l = 0, 1 and 2 phase shifts. The number of bound states is compared with those resulting from detailed spectroscopic studies on the singlet potential and photoassociation results on the triplet potential. We review the scattering formulae needed to satisfy the Pauli principle for the fermion nuclei of 85Rb and 87Rb and their single unpaired electrons, for all possible initial hyperfine states. Scattering lengths are evaluated and their sensitivity to details of the asymptotic potentials is demonstrated.

DOI
10.1088/0953-4075/39/22/001

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The most accurate theoretical potentials available for the interaction of a pair of ground-state Rb atoms are used to evaluate their ultracold scattering properties. The close relation between the zero-energy scattering phase shifts and the number of bound states in the potential, by Levinson's theorem, is used to assign absolute values to the l = 0, 1 and 2 phase shifts. The number of bound states is compared with those resulting from detailed spectroscopic studies on the singlet potential and photoassociation results on the triplet potential. We review the scattering formulae needed to satisfy the Pauli principle for the fermion nuclei of 85Rb and 87Rb and their single unpaired electrons, for all possible initial hyperfine states. Scattering lengths are evaluated and their sensitivity to details of the asymptotic potentials is demonstrated.
We determine the energies of twelve vibrational levels lying within 20 GHz of the lowest dissociation limit of 85Rb2{}^{85}{\mathrm{Rb}}_{2}85Rb2​ with two-color photoassociation spectroscopy of ultracold 85Rb{}^{85}\mathrm{Rb}85Rb atoms. The levels lie in an energy range for which singlet and triplet states are mixed by the hyperfine interaction. We carry out a coupled channels bound state analysis of the level energies, and derive accurate values for 85Rb2{}^{85}{\mathrm{Rb}}_{2}85Rb2​ interaction parameters. The information obtained is sufficient to allow for quantitative calculations of arbitrary Rb ultracold collision properties.
We report the calculation of the same-species elastic scattering properties for the ultracold rubidium–rubidium ( 85 Rb– 85 Rb) system and the results are compared with other theoretical and experimental results in detail. We present an improved potential for triplet ground states of the Rb 2 molecule, and calculate the scattering lengths a t and the effective range r e using WKB and Numerov methods for two rubidium-85 collisions in the triplet state. Also, we investigate the convergence of these scattering properties, i.e. the dependence on core radius and K 0 parameter using quantum defect theory and the analytic calculations of scattering length obtained by Szmytkowski. In addition, we present evaporative cooling and other results that include phase shift and cross section at zero energy limit.
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.
This thesis reports on calculations of the scattering properties of a variety of ultracold alkali-metal mixtures. In particular, we have calculated the scattering properties of homonuclear mixtures of 85Rb, in a variety of incoming channels, and we have calculated the properties of heteronuclear mixtures of the isotopologues of Rb and Cs, and K and Cs. In general, we are interested in the location and character of Feshbach resonances in these mixtures with a view towards ultracold molecule formation. In 85Rb there is a rich Feshbach structure and potential uses for the resonances that we find, in the scattering lengths of the various incoming channels, are discussed. In 85RbCs there is a rich Feshbach structure and the prospects for ultracold molecule formation using this system are detailed. Similarly, we detail the Feshbach resonances of 87RbCs and discuss our results in the context of the successful formation of ultracold ground-state molecules. In the isotopologues of KCs each system has a rich Feshbach structure and we detail the location and width of the resonances, as well as the potential for ultracold molecule formation using each of the isotopes of potassium. In addition to scattering calculations, we have also calculated the location and character of the highest-lying bound states of each system. We have investigated the energy dependence of the scattering length using accurate coupled-channel calculations on 6Li, 39K and 133Cs to explore the behaviour of the effective range in the vicinity of both broad and narrow Feshbach resonances. We present an alternative parametrization of the effective range and further demonstrate that an analytical form of an energy and magnetic field-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length. Lastly, we examine the effect of additional external fields on alkali-metal collisions and discuss how external fields can be used to manipulate the interaction properties of a system.
Ultracold atoms are increasingly used for high-precision experiments that can be utilized to extract accurate scattering properties. This results in a stronger need to improve on the accuracy of interatomic potentials, and in particular the usually rather inaccurate inner-range potentials. A boundary condition for this short range can be conveniently given via the accumulated phase method. However, in this approach one should satisfy three conditions, two of which are in principle conflicting, and the validity of these approximations comes under stress when higher precision is required. We show that a better compromise between the two is possible by allowing for an adiabatic change in the hyperfine mixing of singlet and triplet states for interatomic distances smaller than the separation radius. Results we presented previously in a brief publication using this method show a high precision and extend the set of predicted quantities. The purpose of this paper is to describe its background. A mass-scaling approach to relate accumulated phase parameters in a combined analysis of isotopically related atom pairs is described in detail and its accuracy is estimated, taking into account both Born-Oppenheimer and Wentzel-Kramers-Brillouin breakdown. We demonstrate how numbers of singlet and triplet bound states follow from the mass scaling.
The calculation of the elastic scattering properties of mixtures composed of ultracold Rb–K atoms is reported and compared with experimental results in detail. The improved potentials for both the singlet and triplet molecular states of Rb–K are presented, and the scattering lengths a t and the effective range r e are calculated with numeric and semiclassical methods for Rb–K in the triplet and singlet state. In addition, the convergence of these scattering properties depending on a K 0 parameter is investigated using quantum defect theory. Other results of the evaporative cooling that include the cross section and the spin–charge cross section, the rate coefficient as a function of the energy and ultralow temperature are also presented in this study.