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Atoms

Loading a Paul Trap: Densities, Capacities, and Scaling in the Saturation Regime

R. Blümel

Published Jan 29, 2021• 2 citations
Publisher

Abstract

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.

DOI
10.3390/atoms9010011

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

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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 $q$, (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.

arXiv:1701.04115•Physical Review A•May 24, 2017•7 citations

Universal nonmonotonic structure in the saturation curves of magneto-optical-trap-loaded Na+ ions stored in an ion-neutral hybrid trap: Prediction and observation

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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 ${\mathrm{Na}}^{+}$ ions stored in a hybrid ion-neutral trap and numerically with the help of detailed ab initio molecular-dynamics simulations.

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Scattering and Sympathetic Cooling within an Ion-Neutral Hybrid Trap

Douglas S. Goodman

Dilute ion-neutral gas mixtures are an interesting system to study due to the rich variety and enormous strength of their scattering interactions, especially in the cold and ultracold regimes. Ion-neutral collisions are dominated by long-range polarization potentials that lead to cross sections several orders of magnitude larger than typical neutral-neutral van der Waals interactions. These large ion-neutral interactions can play an important role in atomic and molecular optical physics, astrophysics, and quantum chemistry. Thanks to advances in theoretical modeling of ion-neutral scattering and the development of new ion-neutral hybrid trapping and cooling technology, interest in this previously unexplored area of cold atomic and molecular physics has surged over the past decade.\nThe ion-neutral hybrid trap, composed of a magneto-optical trap concentric within a linear Paul trap, offers the ideal playground for studying and manipulating ion-neutral interactions over a wide energy range (~ 1 μK - 104 K). This dissertation discusses the development of UConn's hybrid trap, compares experimental measurements of the Na+ - Na system and Ca+ - Na system's low-energy collision rates with previously reported theory, and reports on experimental and simulation results of the sympathetic cooling of Na+ ions by laser cooled Na atoms.

•Jan 1, 2015•0 citations
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 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 ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{R}}_{\mathrm{cut}}$ 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.
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.
Long-range polarization forces between ions and neutral atoms result in large elastic scattering cross sections (e.g., $\ensuremath{\sim}\phantom{\rule{-0.16em}{0ex}}\phantom{\rule{-0.16em}{0ex}}{10}^{6}\phantom{\rule{0.28em}{0ex}}\mathrm{a}.\mathrm{u}.$ for Na\mathrm{Na}Na-Na+{\mathrm{Na}}^{+}Na+ or Na\mathrm{Na}Na-Ca+{\mathrm{Ca}}^{+}Ca+ at cold and ultracold temperatures). This suggests that a hybrid ion-neutral trap should offer a general means for significant sympathetic cooling of atomic or molecular ions. We present simion 7.0 simulation results concerning the advantages and limitations of sympathetic cooling within a hybrid trap apparatus consisting of a linear rf Paul trap concentric with a Na\mathrm{Na}Na magneto-optical trap (MOT). This paper explores the impact of various heating mechanisms on the hybrid system and how parameters related to the MOT, Paul trap, number of ions, and ion species affect the efficiency of the sympathetic cooling.
Abstract Experiments in which ultra-cold neutral atoms and charged ions are overlapped, constitute a new field in atomic and molecular physics, with applications ranging from studying out-of-equilibrium dynamics to simulating quantum many-body systems. The holy grail of ion-neutral systems is reaching the quantum low-energy scattering regime, known as the s-wave scattering. However, in most atom–ion systems, there is a fundamental limit that prohibits reaching this regime. This limit arises from the time-dependent trapping potential of the ion, the Paul trap, which sets a lower collision energy limit which is higher than the s-wave energy. In this work, we studied both theoretically and experimentally, the way the Paul trap parameters affect the energy distribution of an ion that is immersed in a bath of ultra-cold atoms. Heating rates and energy distributions of the ion are calculated for various trap parameters by a molecular dynamics (MD) simulation that takes into account the attractive atom–ion potential. The deviation of the energy distribution from a thermal one is discussed. Using the MD simulation, the heating dynamics for different atom–ion combinations is also investigated. In addition, we performed measurements of the heating rates of a ground-state cooled 88Sr+ ion that is immersed in an ultra-cold cloud of 87Rb atoms, over a wide range of trap parameters, and compare our results to the MD simulation. Both the simulation and the experiment reveal no significant change in the heating for different parameters of the trap. However, in the experiment a slightly higher global heating is observed, relative to the simulation.
Dilute ion-neutral gas mixtures are an interesting system to study due to the rich variety and enormous strength of their scattering interactions, especially in the cold and ultracold regimes. Ion-neutral collisions are dominated by long-range polarization potentials that lead to cross sections several orders of magnitude larger than typical neutral-neutral van der Waals interactions. These large ion-neutral interactions can play an important role in atomic and molecular optical physics, astrophysics, and quantum chemistry. Thanks to advances in theoretical modeling of ion-neutral scattering and the development of new ion-neutral hybrid trapping and cooling technology, interest in this previously unexplored area of cold atomic and molecular physics has surged over the past decade.\nThe ion-neutral hybrid trap, composed of a magneto-optical trap concentric within a linear Paul trap, offers the ideal playground for studying and manipulating ion-neutral interactions over a wide energy range (~ 1 μK - 104 K). This dissertation discusses the development of UConn's hybrid trap, compares experimental measurements of the Na+ - Na system and Ca+ - Na system's low-energy collision rates with previously reported theory, and reports on experimental and simulation results of the sympathetic cooling of Na+ ions by laser cooled Na atoms.