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Atomic rubidium, the workhorse of theoretical collision physics

B. Verhaar, Eric van Kempen, S. J. J. M. F. Kokkelmans

Published May 1, 2008• 0 citations
OpenAlex

Abstract

Since the first realizations of Bose-Einstein condensates in ultracold atomic gases in 1995, the 85Rb and 87Rb atomic species have acted as the workhorses of experimental developments in this field. Parallel to and partly preceding this work the same isotopes figured also as workhorses for successful theoretical attempts aiming at unravelling the needed information on interaction properties like scattering lengths and Feshbach resonances. The purpose of this contribution is to describe recent developments of this theoretical work, based on an adiabatic variant of the accumulated phase method, which gives rise to the most reliable and accurate predictions of interaction properties available to date for any alkali atomic gas. The method can be readily applied to predict interaction properties between two different atomic species, once a limited set of experimental data is available to determine the accumulated phases.

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Feshbach resonances in cold atomic gases

E. G. M. van Kempen

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.

•Jan 1, 2006•1 citation

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James P. Burke, John L. Bohn, Brett D. Esry +1 more

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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 ${}^{39}\mathrm{K}$ 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 ${}^{41}\mathrm{K}$ triplet scattering length makes it a better candidate for condensation at zero magnetic field. The fermionic isotope ${}^{40}\mathrm{K}$ 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.

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Determination of collisional properties of cold Na atoms from analysis of bound-state photoassociation and Feshbach resonance field data

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We review the information on the interactions between cold ground-state Na atoms following from ${\mathrm{Na}}_{2}$ bound states, a Na photoassociation experiment, and a recent observation of field-induced Feshbach resonances in a Na Bose condensate. We obtain a set of Na interaction parameters that is in excellent agreement with all these experimental data. The existing discrepancy between different values for the scattering length ${a}_{1,\ensuremath{-}1}$ of Na atoms in the $|1,\ensuremath{-}1〉$ hyperfine state is resolved. The present interaction parameters enable us to give accurate predictions for the singlet and triplet scattering lengths ${a}_{S}$ and ${a}_{T},$ ${a}_{1,\ensuremath{-}1},$ scattering lengths for collisions between Na atoms in other hyperfine states, and resonance fields of several yet unobserved Feshbach resonances. We find ${a}_{S}=(19.1\ifmmode\pm\else\textpm\fi{}{2.1)a}_{0},{a}_{T}=(65.3\ifmmode\pm\else\textpm\fi{}{0.9)a}_{0},$ and ${a}_{1,\ensuremath{-}1}(B=0)=(55.4\ifmmode\pm\else\textpm\fi{}{1.2)a}_{0}.$

Physical Review A•Jan 1, 1999•54 citations

Ultracold Atomic Interactions and Bose–Einstein Condensation

Daniel J. Heinzen

Atomic interactions play a crucial role in Bose-condensed alkali gases. The condensate self-energy, proportional to the two-body s-wave scattering length, strongly affects the stability and other properties of a condensate. Alkali atom scattering lengths have been determined only during the past few years by a combination of conventional molecular spectroscopy, photoassociation spectroscopy, and ultracold atomic collision studies. In this article, we present a brief review of alkali atom interactions and scattering length determinations.

International Journal of Modern Physics B•Nov 10, 1997•3 citations
Since the first realizations of Bose-Einstein condensates in ultracold atomic gases in 1995, the 85Rb and 87Rb atomic species have acted as the workhorses of experimental developments in this field. Parallel to and partly preceding this work the same isotopes figured also as workhorses for successful theoretical attempts aiming at unravelling the needed information on interaction properties like scattering lengths and Feshbach resonances. The purpose of this contribution is to describe recent developments of this theoretical work, based on an adiabatic variant of the accumulated phase method, which gives rise to the most reliable and accurate predictions of interaction properties available to date for any alkali atomic gas. The method can be readily applied to predict interaction properties between two different atomic species, once a limited set of experimental data is available to determine the accumulated phases.
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.
Collision physics plays a key role in understanding the properties of ultracold gases. First, collisions ensure thermalization in trapped atomic samples, which is essential for the success of evaporative cooling. Second, interactions between atoms determine the equilibrium shape and the dynamics of the condensate once it is formed. Finally collisions limit the achievable spatial densities via inelastic processes, which ultimately determine whether a given atomic species may lead to Bose-Einstein condensation. The purpose of the following lectures is to give a basic introduction to collision physics with a special emphasis on the low temperature aspect of these interactions. We will consider here only binary interactions between atoms since one of the remarkable prop-erties of the physics of ultra-cold dilute gases is that all the macroscopic properties of the system can be directly deduced from the two-body interaction potential. In particular the essential concept of scattering length will be introduced and developped for some simple potentials, using as practical examples experimental results obtained on atomic cesium and rubidium. The present lectures are complementary to the ones given by D. Heinzen where a detailed comparison between the collisional properties of the various alkali atoms will be found, together with explanations of the spectroscopic approaches used in the precise determination of interatomic potentials. 1. – Scattering theory: a brief reminder 1.1. Collision between two particles. – We consider here an elementary collision process between two particles 1 and 2 with the same mass M, interacting through the potential
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 review the information on the interactions between cold ground-state Na atoms following from Na2{\mathrm{Na}}_{2}Na2​ bound states, a Na photoassociation experiment, and a recent observation of field-induced Feshbach resonances in a Na Bose condensate. We obtain a set of Na interaction parameters that is in excellent agreement with all these experimental data. The existing discrepancy between different values for the scattering length ${a}_{1,\ensuremath{-}1}$ of Na atoms in the $|1,\ensuremath{-}1〉$ hyperfine state is resolved. The present interaction parameters enable us to give accurate predictions for the singlet and triplet scattering lengths aS{a}_{S}aS​ and aT,{a}_{T},aT​, ${a}_{1,\ensuremath{-}1},$ scattering lengths for collisions between Na atoms in other hyperfine states, and resonance fields of several yet unobserved Feshbach resonances. We find ${a}_{S}=(19.1\ifmmode\pm\else\textpm\fi{}{2.1)a}_{0},{a}_{T}=(65.3\ifmmode\pm\else\textpm\fi{}{0.9)a}_{0},$ and ${a}_{1,\ensuremath{-}1}(B=0)=(55.4\ifmmode\pm\else\textpm\fi{}{1.2)a}_{0}.$
Atomic interactions play a crucial role in Bose-condensed alkali gases. The condensate self-energy, proportional to the two-body s-wave scattering length, strongly affects the stability and other properties of a condensate. Alkali atom scattering lengths have been determined only during the past few years by a combination of conventional molecular spectroscopy, photoassociation spectroscopy, and ultracold atomic collision studies. In this article, we present a brief review of alkali atom interactions and scattering length determinations.