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Journal of Physics Conference Series

Collisions of trapped ions with ultracold atoms in [YbRb]+systems

H D L Lamb, John Goold, J F McCann, Nathan Wells, I Lane

Published Nov 5, 2012• 0 citations
Publisher

Abstract

We investigate the ultracold, elastic-scattering of a trapped atom and a trapped ion. The low-energy potential surfaces of the [ 174 Yb− 87 Rb] + are estimated and the polarizability and higher-order multipole coefficients are obtained from ab initio calculations. The polarizability of the Ytterbium atom is well reproduced and the scattering length is estimated. The excited-state Yb + -Rb system is analysed in detail with a view to applications in hybrid ion-atom traps.

DOI
10.1088/1742-6596/388/12/122008

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We investigate the ultracold, elastic-scattering of a trapped atom and a trapped ion. The low-energy potential surfaces of the [ 174 Yb− 87 Rb] + are estimated and the polarizability and higher-order multipole coefficients are obtained from ab initio calculations. The polarizability of the Ytterbium atom is well reproduced and the scattering length is estimated. The excited-state Yb + -Rb system is analysed in detail with a view to applications in hybrid ion-atom traps.
In order to study ultracold charge-transfer processes in hybrid atom-ion traps, we have mapped out the potential-energy curves and molecular parameters for several low-lying states of the Rb, Yb+{}^{+}+ system. We employ both a multireference configuration interaction and a full configuration interaction (FCI) approach. Turning points, crossing points, potential minima, and spectroscopic molecular constants are obtained for the lowest five molecular states. Long-range parameters, including the dispersion coefficients, are estimated from our ab initio data. The separated-atom ionization potentials and atomic polarizability of the ytterbium atom (${\ensuremath{\alpha}}_{d}=128.4$ atomic units) are in good agreement with experiment and previous calculations. We present some dynamical calculations for (adiabatic) scattering lengths for the two lowest (Yb, Rb+{}^{+}+) channels that were carried out in our work. However, we find that the pseudopotential approximation is rather limited in validity and only applies to nK temperatures. The adiabatic scattering lengths for both the triplet and singlet channels indicate that both are large and negative in the FCI approximation.
We present accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb^{+}-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-order spin-orbit (SO) interaction as the dominant source of hyperfine relaxation in cold Yb^{+}-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb^{+} immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than is predicted by the Langevin capture theory and display a weak T^{-0.3} temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb^{+}-Li should be used to minimize hyperfine relaxation and decoherence of trapped ions in ultracold atomic gases.
Ultracold hybrid ion–atom traps offer the possibility of microscopic manipulation of quantum coherences in the gas using the ion as a probe. However, inelastic processes, particularly charge transfer can be a significant process of ion loss and has been measured experimentally for the ion immersed in a Rb vapour. We use first-principles quantum chemistry codes to obtain the potential energy curves and dipole moments for the lowest-lying energy states of this complex. Calculations for the radiative decay processes cross sections and rate coefficients are presented for the total decay processes; and . Comparing the semi-classical Langevin approximation with the quantum approach, we find it provides a very good estimate of the background at higher energies. The results demonstrate that radiative decay mechanisms are important over the energy and temperature region considered. In fact, the Langevin process of ion–atom collisions dominates cold ion–atom collisions. For spin-dependent processes [ 1 ] the anisotropic magnetic dipole–dipole interaction and the second-order spin–orbit coupling can play important roles, inducing coupling between the spin and the orbital motion. They measured the spin-relaxing collision rate to be approximately five orders of magnitude higher than the charge-exchange collision rate [ 1 ]. Regarding the measured radiative charge transfer collision rate, we find that our calculation is in very good agreement with experiment and with previous calculations. Nonetheless, we find no broad resonances features that might underly a strong isotope effect. In conclusion, we find, in agreement with previous theory that the isotope anomaly observed in experiment remains an open question.
Charge-transfer cold Yb+{}^{+}++++ Rb collision dynamics is investigated theoretically using high-level ab initio potential energy curves, dipole moment functions, and nonadiabatic coupling matrix elements. Within the scalar-relativistic approximation, the radiative transitions from the entrance $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ to the ground $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ state are found to be the only efficient charge-transfer pathway. The spin-orbit coupling does not open other efficient pathways, but alters the potential energy curves and the transition dipole moment for the $A\ensuremath{-}X$ pair of states. The radiative, as well as the nonradiative, charge-transfer cross sections calculated within the ${10}^{\ensuremath{-}3}--10$ cm${}^{\ensuremath{-}1}$ collision energy range exhibit all features of the Langevin ion-atom collision regime, including a rich structure associated with centrifugal barrier tunneling (orbiting) resonances. Theoretical rate coefficients for two Yb isotopes agree well with those measured by immersing Yb+{}^{+}+ ions in an ultracold Rb ensemble in a hybrid trap. Possible origins of discrepancy in the product distributions and relations to previously studied similar processes are discussed.
We study cold collisions between trapped ions and trapped atoms in the semiclassical (Langevin) regime. Using Yb+{\mathrm{Yb}}^{+}Yb+ ions confined in a Paul trap and Yb atoms in a magneto-optical trap, we investigate charge-exchange collisions of several isotopes over three decades of collision energies down to $3\text{ }\text{ }\ensuremath{\mu}\mathrm{eV}$ (${k}_{B}\ifmmode\times\else\texttimes\fi{}35\text{ }\text{ }\mathrm{mK}$). The minimum measured rate coefficient of $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ is in good agreement with that derived from a Langevin model for an atomic polarizability of 143 a.u.