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Physical Review A

Ultracold scattering properties of the short-lived Rb isotopes

James P. Burke, John L. Bohn

Published Feb 1, 1999• 53 citations
Publisher

Abstract

We compute the scattering properties of rubidium atoms at ultracold temperatures, placing special emphasis on the radioactive isotopes ${}^{82}\mathrm{Rb}{,}^{83}\mathrm{Rb}{,}^{84}\mathrm{Rb},$ and ${}^{86}\mathrm{Rb}.$ In combination with the more ``conventional'' isotope ${}^{87}\mathrm{Rb},$ these species yield a wide variety of scattering behavior, with consequences for creating mixtures of Fermi-Fermi, Fermi-Bose, and Bose-Bose gases. In each of these mixtures we find at least one case where the interspecies scattering lengths can be tuned using an external magnetic field. These results should greatly broaden the prospects for quantum degenerate gases in future experiments.

DOI
10.1103/physreva.59.1303

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•Jan 1, 2006•1 citation
We compute the scattering properties of rubidium atoms at ultracold temperatures, placing special emphasis on the radioactive isotopes 82Rb,83Rb,84Rb,{}^{82}\mathrm{Rb}{,}^{83}\mathrm{Rb}{,}^{84}\mathrm{Rb},82Rb,83Rb,84Rb, and 86Rb.{}^{86}\mathrm{Rb}.86Rb. In combination with the more ``conventional'' isotope 87Rb,{}^{87}\mathrm{Rb},87Rb, these species yield a wide variety of scattering behavior, with consequences for creating mixtures of Fermi-Fermi, Fermi-Bose, and Bose-Bose gases. In each of these mixtures we find at least one case where the interspecies scattering lengths can be tuned using an external magnetic field. These results should greatly broaden the prospects for quantum degenerate gases in future experiments.
We determine the interspecies sss-wave triplet scattering length a3{a}_{3}a3​ for all K-Rb isotopic mixtures by measuring the elastic cross section for collisions between 41K^{\mathrm{41}}\mathrm{K}41K and 87Rb^{87}\mathrm{R}\mathrm{b}87Rb in different temperature regimes. The positive value ${a}_{3}=+{163}_{\ensuremath{-}12}^{+57}{a}_{0}$ ensures the stability against collapse of binary $^{41}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$ Bose-Einstein condensates. For the fermion-boson mixture $^{40}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$, we obtain a large and negative scattering length which implies an efficient sympathetic cooling of the fermionic species down to the degenerate regime.
We perform extensive magnetic Feshbach spectroscopy of an ultracold mixture of fermionic 40K^{40}\mathrm{K}40K and bosonic 87Rb^{87}\mathrm{Rb}87Rb atoms. The magnetic-field locations of 13 interspecies resonances are used to construct a quantum collision model able to predict accurate collisional parameters for all $\mathrm{K}\text{\ensuremath{-}}\mathrm{Rb}$ isotopic pairs. In particular, we determine the interspecies sss-wave singlet and triplet scattering lengths for the $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixture as $(\ensuremath{-}108\ifmmode\pm\else\textpm\fi{}3){a}_{0}$ and $(\ensuremath{-}205\ifmmode\pm\else\textpm\fi{}5){a}_{0}$, respectively. We also predict accurate scattering lengths and the position of Feshbach resonances for the other $\mathrm{K}\text{\ensuremath{-}}\mathrm{Rb}$ isotopic pairs. We discuss the consequences of our results for current and future experiments with ultracold $\mathrm{K}\text{\ensuremath{-}}\mathrm{Rb}$ mixtures.
We calculate binary collision parameters for mixtures of ultracold gases of 85Rb{}^{85}\mathrm{Rb}85Rb and 87Rb{}^{87}\mathrm{Rb}87Rb atoms. We predict a large positive triplet scattering length for mixed-isotope collisions, which implies that a stable mixed-isotope double condensate can be formed by sympathetic evaporative cooling. Moreover, collisions between 85Rb{}^{85}\mathrm{Rb}85Rb and 87Rb{}^{87}\mathrm{Rb}87Rb atoms in the lowest hyperfine manifold exhibit magnetic-field-induced Feshbach resonances which should allow partial control of the interaction between condensates. These considerations make Rb an ideal system for the study of interpenetrating bosonic superfluids.
The hyperfine-state-selected scattering properties of potassium atoms at ultralow temperatures are calculated using interaction potentials gleaned from an analysis of recent photoassociation data. We predict that the small, probably negative value of the 39K{}^{39}\mathrm{K}39K triplet scattering length will hamper efforts to produce a Bose-Einstein condensate, unless experiments utilize a broad, accessible magnetic Feshbach resonance. The large positive value calculated for the 41K{}^{41}\mathrm{K}41K triplet scattering length makes it a better candidate for condensation at zero magnetic field. The fermionic isotope 40K{}^{40}\mathrm{K}40K is also predicted to have a large, positive scattering length for elastic collisions between spin states of experimental interest, implying that it can be efficiently evaporatively cooled to the quantum degenerate regime. In addition, certain spin states possess Feshbach resonances that may enable tuning of its interatomic interactions, possibly leading to the formation of Cooper pairs.
We investigate the elastic scattering properties of strontium atoms at ultracold temperatures. The scattering parameters, such as s-wave scattering lengths, effective ranges and p-wave scattering lengths, are calculated for all stable isotope combinations of Sr atoms by the quantal method and semiclassical method, respectively. Good agreements are obtained. The scattering parameters are very sensitive to small changes of the reduced mass. Due to the repulsive interisotope and intraisotope s-wave scattering length and large elastic cross sections, 84 Sr— 86 Sr mixture is a good candidate to realize Bose—Bose quantum degenerate atomic gases.
The research described in this thesis is part of an international effort with the aim of studying ultracold quantum degenerate gas samples like Bose-Einstein condensates and Fermi degenerate systems, consisting of atoms confined in magnetic or optical traps. The behavior of such samples is governed by the inter-atomic interactions and the resulting properties of the atom-atom scattering. At the relevant temperatures of 1nK to 10µK a key property is the atom-atom scattering length a. In chapter 2 a theoretical method is presented which enables one to describe the interaction and scattering of (ultra)cold atoms to unprecedented precision. It is also unparalleled in comprehensiveness: it allows the prediction of a large and varied set of experimental data for all isotopes of the same element. The method relies on the extraction from experiments of a few (phase) parameters which completely summarize the behavior of the atoms in the (ultra)cold regime. In chapter 3 the method is applied to the "workhorses" of cold-atom physics: the atomic species 85Rb and 87Rb. We extract the foregoing parameters to a very high precision from several recent high precision experiments, allowing us to predict e.g. the 87Rb spinor condensate to be ferromagnetic: a prediction for which the scattering length has to be calculated with a precision better than 1%. We also predict Feshbach resonances at experimentally accessible magnetic field strengths; resonances searched for and found by the experimental group of Rempe. In close collaboration with his group we "fine-tune" the interaction parameters found previously, by making use of only one of the observed resonances. We then obtain agreement with 42 out of the observed 43 resonance field strengths and are able to identify bound states inducing the Feshbach resonances at these locations. Chapter 4 describes the results of this research. With a thorough understanding of the rubidium interactions, we then switch to lithium which has a fermionic (6Li) and a bosonic (7Li) isotope. Both are being used in cold-atom experiments. In chapter 5 we evaluate the interaction parameters for lithium allowing us to predict magnetic field strengths for which a sample of fermionic 6Li atoms can be regarded as strongly interacting. Furthermore, a three-level method for measuring mean-field shifts, based on radio-frequency techniques, is introduced. For weak interactions we find proportionality of resonance shifts to interaction strengths. In the strongly interacting regime, however, these shifts become very small reflecting the quantum unitarity limit and many-body effects. Most interesting is the fact that in this regime the shifts are small both for large positive a and for large negative a, likely reflecting the universality of the interaction energy. In chapters 6 and 7 the interactions between lithium atoms are reinvestigated, making use of newly available experimental data and with the updated interaction parameters special attention is paid to locating field strengths at which magnetically tunable Feshbach resonances occur in the scattering of lithium atoms. In chapter 6 scattering events in a gas of (fermionic) 6Li atoms are studied. In chapter 7 we show that a consistent description of the 6Li+6Li system can be given. We discuss theoretical uncertainties for the position of the wide 6Li Feshbach resonance and present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the 6Li-7Li system, and their importance for different types of crossover superfluidity models is discussed. Molecules created by magnetically sweeping over these resonances will have a fermionic character. One magnetic field strength is predicted at which two different fermionic molecules can be created simultaneously.