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arXiv:1901.00905 · Physical Review A

Thermal atom-ion collisions in a K- Yb+ hybrid system

Thai M. Hoang, Peter D. D. Schwindt, Yuan‐Yu Jau

Published Aug 1, 2019• 2 citations
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Abstract

We present experimental studies of atom-ion collisions using buffer-gas cooled, trapped ytterbium (${\mathrm{Yb}}^{+}$) ions immersed in potassium (K) vapor. The range of the collisional temperature is on the order of several hundred kelvin (thermal regime). We have determined various collisional rate coefficients of the ${\mathrm{Yb}}^{+}$ ion per K-atom number density. We find the upper bounds of charge-exchange rate coefficients ${\ensuremath{\kappa}}_{\mathrm{ce}}$ to be $(12.7\ifmmode\pm\else\textpm\fi{}1.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$ for K-$^{171}\mathrm{Yb}^{+}$ and $(5.3\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$ for K-$^{172}\mathrm{Yb}^{+}$. For both isotopes, the spin-destruction rate coefficient ${\ensuremath{\kappa}}_{\mathrm{sd}}$ has an upper bound at $(1.46\ifmmode\pm\else\textpm\fi{}0.77)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$. The spin-exchange rate coefficient ${\ensuremath{\kappa}}_{\mathrm{se}}$ is measured to be $(1.64\ifmmode\pm\else\textpm\fi{}0.51)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}$. The relatively low charge-exchange rate reported here demonstrates the advantage of using K atoms to sympathetically cool ${\mathrm{Yb}}^{+}$ ions and the relatively high spin-exchange rate may benefit research work in quantum metrology and quantum information processing on an atom-ion platform using K atoms and ${\mathrm{Yb}}^{+}$ ions.

DOI
10.1103/physreva.100.022701

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We present experimental studies of atom-ion collisions using buffer-gas cooled, trapped ytterbium (Yb+{\mathrm{Yb}}^{+}Yb+) ions immersed in potassium (K) vapor. The range of the collisional temperature is on the order of several hundred kelvin (thermal regime). We have determined various collisional rate coefficients of the Yb+{\mathrm{Yb}}^{+}Yb+ ion per K-atom number density. We find the upper bounds of charge-exchange rate coefficients \ensuremathκce{\ensuremath{\kappa}}_{\mathrm{ce}}\ensuremathκce​ to be (12.7\ifmmode±\else\textpm\fi1.6)\ifmmode×\else\texttimes\fi10\ensuremath−14cm3s\ensuremath−1(12.7\ifmmode\pm\else\textpm\fi{}1.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}(12.7\ifmmode±\else\textpm\fi1.6)\ifmmode×\else\texttimes\fi10\ensuremath−14cm3s\ensuremath−1 for K-171Yb+^{171}\mathrm{Yb}^{+}171Yb+ and (5.3\ifmmode±\else\textpm\fi0.7)\ifmmode×\else\texttimes\fi10\ensuremath−14cm3s\ensuremath−1(5.3\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}(5.3\ifmmode±\else\textpm\fi0.7)\ifmmode×\else\texttimes\fi10\ensuremath−14cm3s\ensuremath−1 for K-172Yb+^{172}\mathrm{Yb}^{+}172Yb+. For both isotopes, the spin-destruction rate coefficient \ensuremathκsd{\ensuremath{\kappa}}_{\mathrm{sd}}\ensuremathκsd​ has an upper bound at (1.46\ifmmode±\else\textpm\fi0.77)\ifmmode×\else\texttimes\fi10\ensuremath−9cm3s\ensuremath−1(1.46\ifmmode\pm\else\textpm\fi{}0.77)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}(1.46\ifmmode±\else\textpm\fi0.77)\ifmmode×\else\texttimes\fi10\ensuremath−9cm3s\ensuremath−1. The spin-exchange rate coefficient \ensuremathκse{\ensuremath{\kappa}}_{\mathrm{se}}\ensuremathκse​ is measured to be (1.64\ifmmode±\else\textpm\fi0.51)\ifmmode×\else\texttimes\fi10\ensuremath−9cm3s\ensuremath−1(1.64\ifmmode\pm\else\textpm\fi{}0.51)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}(1.64\ifmmode±\else\textpm\fi0.51)\ifmmode×\else\texttimes\fi10\ensuremath−9cm3s\ensuremath−1. The relatively low charge-exchange rate reported here demonstrates the advantage of using K atoms to sympathetically cool Yb+{\mathrm{Yb}}^{+}Yb+ ions and the relatively high spin-exchange rate may benefit research work in quantum metrology and quantum information processing on an atom-ion platform using K atoms and Yb+{\mathrm{Yb}}^{+}Yb+ ions.
Long-lived metastable states of Yb+{\text{Yb}}^{+}Yb+ ions are used for atomic frequency standards, precision measurements, and quantum information research. The effect of population trapping and transfer in these states must be well understood. We report here the transfer of Yb+{\text{Yb}}^{+}Yb+ ions into the long-lived 2F7/2{^{2}F}_{7/2}2F7/2​ state by means of collisions between He buffer gas and Yb+{\text{Yb}}^{+}Yb+ ions held in a linear Paul trap. Transfer rates were measured as functions of buffer-gas pressure and repump-laser power, and the collisional population transfer rates were extracted. The measured transfer rate coefficients are $8.32(75)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and $8.65(33)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }{\text{cm}}^{3}/\text{s}$ for the collisional processes ${^{2}P}_{1/2}\ensuremath{\rightarrow}{^{2}D}_{5/2}$ and ${^{2}D}_{3/2}\ensuremath{\rightarrow}{^{2}F}_{7/2}$, respectively.
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.
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.
We report on the observation of cold collisions between 6Li^{6}\mathrm{Li}6Li atoms and Yb+{\mathrm{Yb}}^{+}Yb+ ions. This combination of species has recently been proposed as the most suitable for reaching the quantum limit in hybrid atom-ion systems, due to its large mass ratio. For atoms and ions prepared in the 2S1/2^{2}S_{1/2}2S1/2​ ground state, the charge-transfer and association rate is found to be at least 103{10}^{3}103 times smaller than the Langevin collision rate. These results confirm the excellent prospects of $^{6}\mathrm{Li}\ensuremath{-}{\mathrm{Yb}}^{+}$ for sympathetic cooling and quantum information applications. For ions prepared in the excited electronic states 2P1/2,2D3/2^{2}P_{1/2}, ^{2}D_{3/2}2P1/2​,2D3/2​, and 2F7/2^{2}F_{7/2}2F7/2​, we find that the reaction rate is dominated by charge transfer and does not depend on the ionic isotope or the collision energy in the range $\ensuremath{\sim}1--120\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$. The low charge-transfer rate for ground-state collisions is corroborated by theory, but the 4f4f4f shell in the Yb+{\mathrm{Yb}}^{+}Yb+ ion prevents an accurate prediction for the charge-transfer rate of the 2P1/2,2D3/2^{2}P_{1/2}, ^{2}D_{3/2}2P1/2​,2D3/2​, and 2F7/2^{2}F_{7/2}2F7/2​ states. Using ab initio methods of quantum chemistry we calculate the atom-ion interaction potentials up to energies of $30\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, and use these to give qualitative explanations of the observed rates.
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.