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arXiv:0806.4002 · Physical Review A

Quantum theory of ultracold atom-ion collisions

Zbigniew Idziaszek, Tommaso Calarco, Paul S. Julienne, Andrea Simoni

Published Jan 15, 2009• 124 citations
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Abstract

We study atom-ion scattering in the ultracold regime. To this aim, an analytical model based on the multichannel quantum-defect formalism is developed and compared to close-coupled numerical calculations. We investigate the occurrence of magnetic Feshbach resonances, focusing on the specific $^{40}\mathrm{Ca}^{+}+\mathrm{Na}$ system. The presence of several resonances at experimentally accessible magnetic fields should allow the atom-ion interaction to be precisely tuned. A fully quantum-mechanical study of charge-exchange processes shows that charge-exchange rates should remain small even in the presence of resonance effects. Most of our results can be cast in a system-independent form and are important for the realization of charge-neutral ultracold systems.

DOI
10.1103/physreva.79.010702

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We study atom-ion scattering in the ultracold regime. To this aim, an analytical model based on the multichannel quantum-defect formalism is developed and compared to close-coupled numerical calculations. We investigate the occurrence of magnetic Feshbach resonances, focusing on the specific 40Ca++Na^{40}\mathrm{Ca}^{+}+\mathrm{Na}40Ca++Na system. The presence of several resonances at experimentally accessible magnetic fields should allow the atom-ion interaction to be precisely tuned. A fully quantum-mechanical study of charge-exchange processes shows that charge-exchange rates should remain small even in the presence of resonance effects. Most of our results can be cast in a system-independent form and are important for the realization of charge-neutral ultracold systems.
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.
Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized by simple parameters. Our formula is in excellent agreement with numerical coupled-channel calculations for several cases of overlapping resonances in the collisions of two 7{}^{7}7Li atoms or two Cs atoms.
We investigate the prospects of using magnetic Feshbach resonance to control charge exchange in ultracold collisions of heteroisotopic combinations of atoms and ions of the same element. The proposed treatment, readily applicable to alkali or alkaline-earth metals, is illustrated on cold collisions of 9Be+^{9}\mathrm{Be}^{+}9Be+ and 10Be^{10}\mathrm{Be}10Be. Feshbach resonances are characterized by quantum scattering calculations in a coupled-channel formalism that includes non-Born-Oppenheimer terms originating from the nuclear kinetic operator. Near a resonance predicted at 322 G, we find the charge exchange rate coefficient to rise from practically zero to values greater than ${10}^{\ensuremath{-}12}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}$/s. Our results suggest controllable charge exchange processes between different isotopes of suitable atom-ion pairs, with potential applications to quantum systems engineered to study charge diffusion in trapped cold atom-ion mixtures and emulate many-body physics.
Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave lll and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary lll, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary lll, (b) rigorous definitions of ``broad'' and ``narrow'' resonances of arbitrary lll and their different scattering characteristics, and (c) the tuning of the effective range and the generalized effective range by a magnetic field.
We explore collisions of atomic particles in two different regimes. In the first part of this work, we study atom-atom collisions of alkali metals at ultracold temperatures and conditions typically found in modern experiments. Feshbach resonances induced by external magnetic fields present a way to change collisional properties and exhibit control over cold collisions. We perform a fully quantum coupled-channel calculation in molecular orbital formalism to calculate collisional properties and characterize Feshbach resonances in ultracold Li+Na and Li+Rb systems. Furthermore, we use the results of these calculations as a foundation to propose a novel scheme for formation of stable ultracold molecules in their lowest rovibrational level. The formation scheme relies on the fact that the photoassociation rate becomes greatly enhanced in the vicinity of a Feshbach resonance, resulting in a large increase of the number of produced excited molecules. Efficient production of stable ultracold molecules is a prerequisite for realization of various proposed platforms for quantum computing with neutral atoms and molecules. In addition, we suggest a way to exploit specifics of the photoassociation rate behavior near its minimum for a precision measurement experiment to detect hypothetical variation of the electron-proton mass ratio in time. ^ The second part of this study examines ion-atom collisions in our solar system. Highly charged ions present in the solar wind collide with neutrals, capture one or more electrons into high excited states and deexcite, radiating energetic X-ray and UV photons. In particular, we study X-ray emissions charge-exchange collisions between fully stripped C6+, N7+ and O8+ solar wind ions and heliospheric hydrogen. We analytically solve the two-center Schrödinger equation and construct electronic potential curves for the aforementioned molecular ions. Subsequently, we compute polarization of the X-rays emitted in a single-step deexcitation following charge-exchange collisions and construct a polarization map for the ecliptic plane, as observed from Earth. Our analysis indicates that the heliospheric charge-exchange X-rays are slightly polarized, with the polarization P close to ten percent for the optimal line-of-sight. ^
We present a theoretical model for describing ultracold atomic collision based on the multichannel quantum-defect theory. An analytical expression for the quantum-defect matrix Y is derived for the truncated 1/R61/{R}^{6}1/R6 model potential, and threshold behaviors of the quantum-defect parameters are discussed. The model allows us to predict the Feshbach resonances when the singlet and triplet scattering lengths are known or to fit the scattering lengths when a couple of Feshbach resonances is located experimentally. As an illustrative example, we investigate the 6{}^{6}6Li-40{}^{40}40K scattering. The theoretical results agree quite well with experimental values.