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arXiv:1002.1022 · Physical Review Letters

Universal Properties in Ultracold Ion-Atom Interactions

Bo Gao

Published May 25, 2010• 72 citations
arXivHTMLPDF

Abstract

We present some of the universal properties in ion-atom interaction derived from a newly formulated quantum-defect theory for the -1/r4 type of long-range interactions. For bound states, we present the universal bound spectrum, namely, the equivalent of the Rydberg formula, for ion-atom systems. For scattering, we introduce the concept of a universal resonance spectrum to give a systematic understanding of many resonances present in ion-atom scattering. The theory further provides a method for an accurate spectroscopic determination of the atomic polarizability. It also suggests the existence of atomlike molecules, in which multiple atoms orbit around a heavy ion.

DOI
10.1103/physrevlett.104.213201

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We present some of the universal properties in ion-atom interaction derived from a newly formulated quantum-defect theory for the -1/r4 type of long-range interactions. For bound states, we present the universal bound spectrum, namely, the equivalent of the Rydberg formula, for ion-atom systems. For scattering, we introduce the concept of a universal resonance spectrum to give a systematic understanding of many resonances present in ion-atom scattering. The theory further provides a method for an accurate spectroscopic determination of the atomic polarizability. It also suggests the existence of atomlike molecules, in which multiple atoms orbit around a heavy ion.
Ultracold collisions of cold atoms or molecules make the bound states of the collision complex formed from the two colliding species accessible for control and manipulation of the cold species or the complex. Such resonances are best treated by a resonant scattering theory, which in the ultracold domain can take advantage of the properties of the long-range potential and the methods of multichannel quantum defect theory. Coupled channels calculations on the threshold scattering states and bound states of the 40 K 87 Rb molecule illustrate the ideas and methodology of quantum defect theory using the long-range potential and also demonstrate the spin properties of the bound states throughout the spectrum. 1
Ultracold collisions of cold atoms or molecules make the bound states of the collision complex formed from the two colliding species accessible for control and manipulation of the cold species or the complex. Such resonances are best treated by a resonant scattering theory, which in the ultracold domain can take advantage of the properties of the long-range potential and the methods of multichannel quantum defect theory. Coupled channels calculations on the threshold scattering states and bound states of the 40K87Rb molecule illustrate the ideas and methodology of quantum defect theory using the long-range potential and also demonstrate the spin properties of the bound states throughout the spectrum.
We propose a novel experimental method to extend the investigation of ion-atom collisions from the so far studied cold, essentially classical regime to the ultracold, quantum regime. The key aspect of this method is the use of Rydberg molecules to initialize the ultracold ion-atom scattering event. We exemplify the proposed method with the lithium ion-atom system, for which we present simulations of how the initial Rydberg molecule wave function, freed by photoionization, evolves in the presence of the ion-atom scattering potential. We predict bounds for the ion-atom scattering length from ab initio calculations of the interaction potential. We demonstrate that, in the predicted bounds, the scattering length can be experimentally determined from the velocity of the scattered wave packet in the case of ^{6}Li^{+}-^{6}Li and from the molecular ion fraction in the case of ^{7}Li^{+}-^{7}Li. The proposed method to utilize Rydberg molecules for ultracold ion-atom scattering, here particularized for the lithium ion-atom system, is readily applicable to other ion-atom systems as well.
Rydberg molecule, formed by one or more Rydberg atoms, exhibits remarkable properties, including an exceptionally large spatial extent, rich rovibrational level structures, permanent electric dipole moments, and a pronounced sensitivity to external fields. Based on the underlying binding mechanisms, Rydberg molecules can be divided into three categories, the ground-Rydberg molecule that is bound via a low-energy electron-atom scattering interaction between ground atom and Rydberg electron, the Rydberg-Rydberg molecule that is bound via a long-range electrostatic interaction between Rydberg atoms, and the ion-Rydberg molecule that is bound via single- or multi-polar interactions between Rydberg atom and ion. This review focuses on recent theoretical and experimental advances in diatomic Rydberg molecules, covering their formation and binding mechanisms, potential energy curves, experimental observations, and spectroscopic properties, with the aim of providing a comprehensive overview of the current state and future prospects of this rapidly developing field.
We calculate the bound and scattering properties of a system of two neutral atoms and an ion near an ion-atom Feshbach resonance. Our results indicate that long-range ion-atom interactions lead to significant deviations from universal behavior derived from contact or van der Waals potentials. We find that ionic systems display an overall suppression of inelastic transitions leading to recombination rates and lifetimes of Efimov state orders of magnitude larger with respect to those for neutral atoms. We further characterize the dense spectra of triatomic molecular ions with extended lifetimes. Our results provide a deeper insight into the universality and structure of three-body ionic systems and establish them as a promising platform for exploring novel few- and many-body phenomena with long-range interactions.
We develop an analytical model for ultracold atom–ion collisions using the multichannel quantum-defect formalism. The model is based on analytical solutions of the r −4 long-range potential and on the application of a frame transformation between asymptotic and molecular bases. This approach allows the description of atom–ion interaction in the ultracold domain in terms of only three parameters: the singlet and triplet scattering lengths, assumed to be independent of the relative motion angular momentum, and the lead dispersion coefficient of the asymptotic potential. We also introduce corrections to the scattering lengths that improve the accuracy of our quantum-defect model for higher-order partial waves, a particularly important result for an accurate description of shape and Feshbach resonances at finite temperature. The theory is applied to the system composed of a 40 Ca + ion and a Na atom, and compared with numerical coupled-channel calculations carried out using ab initio potentials. For this particular system, we investigate the spectrum of bound states, the rate of charge-transfer processes and the collision rates in the presence of magnetic Feshbach resonances at zero and finite temperature.