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arXiv:1701.04115 · Physical Review A

Loading a linear Paul trap to saturation from a magneto-optical trap

James E. Wells, R. Blümel, Jonathan M. Kwolek, D. S. Goodman, W. W. Smith

Published May 24, 2017• 7 citations
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Abstract

We present experimental measurements of the steady-state ion number in a linear Paul trap (LPT) as a function of the ion-loading rate. These measurements, taken with (a) constant Paul trap stability parameter $q$, (b) constant radio-frequency (rf) amplitude, or (c) constant rf frequency, show nonlinear behavior. At the loading rates achieved in this experiment, a plot of the steady-state ion number as a function of loading rate has two regions: a monotonic rise (region I) followed by a plateau (region II). Also described are simulations and analytical theory which match the experimental results. Region I is caused by rf heating and is fundamentally due to the time dependence of the rf Paul-trap forces. We show that the time-independent pseudopotential, frequently used in the analytical investigation of trapping experiments, cannot explain region I, but explains the plateau in region II and can be used to predict the steady-state ion number in that region. An important feature of our experimental LPT is the existence of a radial cutoff ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{R}}_{\mathrm{cut}}$ that limits the ion capacity of our LPT and features prominently in the analytical and numerical analysis of our LPT-loading results. We explain the dynamical origin of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{R}}_{\mathrm{cut}}$ and relate it to the chaos border of the fractal of non-escaping trajectories in our LPT. We also present an improved model of LPT ion-loading as a function of time.

DOI
10.1103/physreva.95.053416

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We present experimental measurements of the steady-state ion number in a linear Paul trap (LPT) as a function of the ion-loading rate. These measurements, taken with (a) constant Paul trap stability parameter qqq, (b) constant radio-frequency (rf) amplitude, or (c) constant rf frequency, show nonlinear behavior. At the loading rates achieved in this experiment, a plot of the steady-state ion number as a function of loading rate has two regions: a monotonic rise (region I) followed by a plateau (region II). Also described are simulations and analytical theory which match the experimental results. Region I is caused by rf heating and is fundamentally due to the time dependence of the rf Paul-trap forces. We show that the time-independent pseudopotential, frequently used in the analytical investigation of trapping experiments, cannot explain region I, but explains the plateau in region II and can be used to predict the steady-state ion number in that region. An important feature of our experimental LPT is the existence of a radial cutoff R\ifmmode^\elseˆ\ficut{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{R}}_{\mathrm{cut}}R\ifmmode^\elseˆ\fi​cut​ that limits the ion capacity of our LPT and features prominently in the analytical and numerical analysis of our LPT-loading results. We explain the dynamical origin of R\ifmmode^\elseˆ\ficut{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{R}}_{\mathrm{cut}}R\ifmmode^\elseˆ\fi​cut​ and relate it to the chaos border of the fractal of non-escaping trajectories in our LPT. We also present an improved model of LPT ion-loading as a function of time.
Providing ideal conditions for the study of ion-neutral collisions, we investigate here the properties of the saturated, steady state of a three-dimensional Paul trap, loaded from a magneto-optic trap. In particular, we study three assumptions that are sometimes made under saturated, steady-state conditions: (i) The pseudopotential provides a good approximation for the number, Ns, of ions in the saturation regime, (ii) the maximum of Ns occurs at a loading rate of approximately 1 ion per rf cycle, and (iii) the ion density is approximately constant. We find that none of these assumptions are generally valid. However, based on detailed classical molecular dynamics simulations, and as a function of loading rate and trap control parameter, we show where to find convenient dynamical regimes for ion-neutral collision experiments, or how to rescale to the pseudo-potential predictions. We also investigate the fate of the electrons generated during the loading process and present a new heating mechanism, insertion heating, that in some regimes of trapping and loading may rival and even exceed the rf-heating power of the trap.
We predict that the maximal, steady-state ion capacity ${N}_{s}(\ensuremath{\lambda})$ of radio-frequency (rf) traps, loaded at a rate of $\ensuremath{\lambda}$ particles per rf cycle, shows universal, nonlinear, nonmonotonic behavior as a function of loading rate $\ensuremath{\lambda}$. The shape of ${N}_{s}(\ensuremath{\lambda})$, characterized by four dynamical regimes, is universal; i.e., it is predicted to manifest itself in all types of rf traps independent of the details of their construction and independent of particle species loaded. For $\ensuremath{\lambda}\ensuremath{\ll}$ 1 (region I), as expected, ${N}_{s}(\ensuremath{\lambda})$ increases monotonically with $\ensuremath{\lambda}$. However, contrary to intuition, at intermediate $\ensuremath{\lambda}\ensuremath{\sim}1$ (region II), ${N}_{s}(\ensuremath{\lambda})$ reaches a maximum, followed by a local minimum of ${N}_{s}(\ensuremath{\lambda})$ (region III). For $\ensuremath{\lambda}\ensuremath{\gg}1$ (region IV), ${N}_{s}(\ensuremath{\lambda})$ again rises monotonically. In region IV, numerical simulations, analytical calculations, and experiments show ${N}_{s}(\ensuremath{\lambda})\ensuremath{\sim}{\ensuremath{\lambda}}^{2/3}$. We confirm our predictions both experimentally with magneto-optical-trap-loaded Na+{\mathrm{Na}}^{+}Na+ ions stored in a hybrid ion-neutral trap and numerically with the help of detailed ab initio molecular-dynamics simulations.
Linear Paul traps use radio frequency fields to confine ions for long times in deep potentials. The simplicity and versatility of these devices has led to their use in a wide variety of fields, from mass spectroscopy to quantum information. Within the past fifteen years, beginning with pioneering work at UConn, Paul traps have been combined with atom traps to form hybrid atom-ion traps. Hybrid traps serve as platforms for measuring ion-atom interaction rates, sympathetically cooling atomic and molecular ions, and studying the behavior of trapped ions. This work discusses simulations, analytical theory, and experiments in a hybrid trap that show a previously unknown dynamical effect in a population of trapped ions. The steady state trapped ion number in a Paul trap is non-monotonic with the loading rate of the Paul trap. This effect is universal to both Linear and 3D Paul traps and is likely to be found in other types of ion traps as well because it is the result of the Coulomb interaction in the presence of a trap. This behavior also affects the decay of ions from the trap. Understanding the loading and decay behavior from a saturated Linear Paul trap is important for the study of ion-atom interactions in a hybrid trap when the ions lack optical transitions.
We present model-independent measurements of the excited-state population of atoms in a sodium (Na) magneto-optical trap (MOT) using a hybrid ion-neutral trap composed of a MOT and a linear Paul trap (LPT). We photoionize excited Na atoms trapped in the MOT and use two independent methods to measure the resulting ions: directly by trapping them in our LPT, and indirectly by monitoring changes in MOT fluorescence. By measuring the ionization rate via these two independent methods, we have enough information to directly determine the population of MOT atoms in the excited state. The resulting measurement reveals that there is a range of trapping-laser intensities where the excited-state population of atoms in our MOT follows the standard two-level model intensity dependence. However, an experimentally determined effective saturation intensity must be used instead of the theoretically predicted value from the two-level model. We measured the effective saturation intensity to be ${I}_{\mathrm{SE}}=22.9\ifmmode\pm\else\textpm\fi{}5.1\phantom{\rule{0.222222em}{0ex}}\mathrm{mW}/{\mathrm{cm}}^{2}$ for the type-I Na MOT and ${I}_{\mathrm{SE}}=49\ifmmode\pm\else\textpm\fi{}11\phantom{\rule{0.28em}{0ex}}\mathrm{mW}/{\mathrm{cm}}^{2}$ for the type-II Na MOT, approximately 1.7 and 3.6 times the theoretical estimate, respectively. Lastly, at large trapping-laser intensities, our experiment reveals a clear departure from the two-level model at a critical intensity that we believe is due to a state-mixing effect, the critical intensity of which can be determined by a simple power broadening model.
In order to demonstrate laser cooling on negatively charged ions, it is necessary to confine the ions in a region free of strong magnetic fields. In the course of this thesis, the pre-existing design of a linear Paul trap was modified and taken into operation. The new design possesses two additional end cap electrodes whose shape provides effective axial confinement without blocking optical access to the trapped particles. The influence of these end cap electrodes on the trapping potential was simulated and compared to experimental results. Measurements with AU- ions show that the trap allows storage of ions for multiple hours. Analysis ofthe storage time suggests that the loading process heats up the trapped ions. The lifetime τHot of the hot ions was determined to be 23(3) min. After thermalization, the lifetime increases to 75(2) min. Measurements of the ion cloud’s radius provide an estimation of the equilibrium temperature T∞ ≈5000 K. The experimentally determined time constant of the cooling process is τcool = 41:6(4) s.
Sympathetic laser cooling of ions stored within a linear-geometry, radio frequency, electric-quadrupole trap has been investigated using computational and theoretical techniques. The simulation, which allows five sample ions to interact with 35 laser-cooled atomic ions, revealed an instability heating mechanism, which can prevent ions below a certain critical mass from being sympathetically cooled. This critical mass can, however, be varied by changing the trapping field parameters, thus allowing ions with a very large range of masses to be sympathetically cooled using a single ion species. A theoretical explanation of this instability heating mechanism is presented which predicts that the cooling-heating boundary in trapping parameter space is a line of constant qu{q}_{u}qu​ (ion trap stability coefficient), a result supported by the computational results. The threshold value of qu{q}_{u}qu​ depends on the masses of the interacting ions. A functional form of this dependence is given.