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arXiv:0808.3620 · Physical Review Letters

Observation of Cold Collisions between Trapped Ions and Trapped Atoms

Andrew T. Grier, Marko Cetina, Fedja Oručević, Vladan Vuletić

Published Jun 4, 2009• 262 citations
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Abstract

We study cold collisions between trapped ions and trapped atoms in the semiclassical (Langevin) regime. Using ${\mathrm{Yb}}^{+}$ 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.

DOI
10.1103/physrevlett.102.223201

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We report the measurement of collision rate coefficient for collisions between ultracold Cs atoms and low-energy Cs+\mathrm{C}{\mathrm{s}}^{+}Cs+ ions. The experiments are performed in a hybrid trap consisting of a magneto-optical trap (MOT) for Cs atoms and a Paul trap for Cs+\mathrm{C}{\mathrm{s}}^{+}Cs+ ions. The ion-atom collisions impart kinetic energy to the ultracold Cs atoms, resulting in their escape from the shallow MOT and, therefore, in a reduction in the number of Cs atoms in the MOT. By monitoring, using fluorescence measurements, the Cs atom number, and the MOT loading dynamics and then fitting the data to a rate equation model, the ion-atom collision rate is derived. The $\mathrm{Cs}\ensuremath{-}\mathrm{C}{\mathrm{s}}^{+}$ collision rate coefficient $9.3(\ifmmode\pm\else\textpm\fi{}0.4)(\ifmmode\pm\else\textpm\fi{}1.2)(\ifmmode\pm\else\textpm\fi{}3.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{3}\phantom{\rule{0.28em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, measured for an ion distribution with most probable collision energy of 95 meV $(\ensuremath{\approx}{\mathrm{k}}_{\mathrm{B}}\phantom{\rule{4pt}{0ex}}1100\phantom{\rule{4pt}{0ex}}\mathrm{K})$, is in fair agreement with theoretical calculations. As an intermediate step, we also determine the photoionization cross section of Cs 6P3/26{P}_{3/2}6P3/2​ atoms at 473 nm wavelength to be $2.28(\ifmmode\pm\else\textpm\fi{}0.33)\phantom{\rule{4pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{2}$.
Over the recent years a new research field emerged that combines technologies for cooling and trapping of neutral atoms and charged ions in one experimental apparatus. These atom-ion hybrid traps enable the investigation of atom-ion interactions at unprecedentedly low collision energies targeting the ultracold s-wave regime. In this thesis I report on experiments performed in an hybrid atom-ion apparatus combining single Ba^+ or Rb^+ ions with ultracold neutral Rb atoms. The main focus of this work is studying the emerging three-body reaction dynamics in a cold charged gas. First, I will present measurements investigating cold reactions in the hetero-nuclear Ba^+ - Rb system. So far, most theoretical and experimental studies have been dealing with reactions between two particles. However, we find that three-body reactions already dominate over two-body ones at atomic densities down to 10^{−11} cm^{−3} once collision energies are in the low mK regime. We then investigate the energy scaling of inelastic ternary collisions between an ion and two atoms. A power-law scaling of the three-body rate coefficient is predicted by theory. We find agreement with the experiment if we include the ion’s kinetic energy distribution that we access numerically. The next study elaborates on the very first observation of ternary reactions in a hybrid cold atom-ion setup. For this we immerse a single Rb^+ ion into ultracold Rb atoms with sufficiently reduced excess micromotion. Occurring reactions are signaled by the creation of highly energetic Rb^+ ions. I will also showcase novel techniques to investigate the atom and the ion system by using the respective other one which were developed by us over the course of the last years. In order to reduce the total ion kinetic energy in a Paul trap one has to compensate the ion’s excess micromotion. This is routinely being done by analyzing the ion’s fluorescence. By observing collision energy dependent elastic atom-ion collisions in an ultracold atom cloud we directly infer the ion’s micromotion energy. This way we can perform atom-ion experiments with optically dark Rb^+ ions and good excess micromotion. Without the need of visible laser light for micromotion compensation we are able to investigate the evolution of quasi-static stray electric fields in a Paul trap over a period of several months. The last study I will present is targeted at neutral Rb only. There, we spectroscopically access the molecular state distribution of Rb_2 molecules formed in neutral three-body recombination by state-selective ionization of these molecules. Trapping and subsequent detection of these ions is being done with our Paul trap, which has the role of a very sensitive single ion detector in these measurements.
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 ${\ensuremath{\kappa}}_{\mathrm{ce}}$ 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-171Yb+^{171}\mathrm{Yb}^{+}171Yb+ 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-172Yb+^{172}\mathrm{Yb}^{+}172Yb+. 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 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.
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.