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Loading and Decay of Ions from a Linear Paul Trap

James E. Wells

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

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.

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Scattering and Sympathetic Cooling within an Ion-Neutral Hybrid Trap

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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
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.
Advances in research in fields such as quantum information and quantum chemistry require subtle methods for trapping particles, including ions, neutral atoms, and molecules. Here, we propose a hybrid ion-trapping method that combines a Paul trap with optical tweezers. This trap incorporates both the deep-potential characteristic of the Paul trap and the micromotion-free nature of the optical dipole trap. By modulating the optical dipole trap synchronously with the radio-frequency voltage of the Paul trap, the alternating electrical force in the trap center is fully counteracted, and the micromotion temperature of a cold trapped ion can reach the nanokelvin scale, while the trap depth exceeds 300 K. These features will allow cold collisions between an ion and an atom in the sss-wave regime and stably trap the produced molecular ion in the cold hybrid system. This provides a unique platform for probing the interactions between the ions and the surrounding neutral particles and enables the investigation of new reaction pathways and reaction products in the cold regime.
We have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V.S. Melezhik et. al., Phys. Rev. A100, 063406 (2019)). The important element of the hybrid atom-ion systems is the electromagnetic Paul trap confining the charged ion. The oscillating motion of the confined ion is defined by two frequencies of the Paul trap. It is the frequency of the order of 100 kHz due to the constant electric field and the radio-frequency of about 1-2 MHz defined by the alternating electromagnetic field of the ion trap. The necessity to accurately treat the ion motion in the combined field with two time scales defined by these two very different frequencies has demanded to develop the stable computational scheme for integration of the classical Hamilton equations for the ion motion. Moreover, the scheme must be stable on rather long time-interval of the ion collision with the cold atom ∼ 10 × 2/ defined by the atomic trap frequency ∼ 10 kHz and in the moment of the atom-ion collision when the Hamilton equations are strongly coupled. The developed numerical method takes into account all these features of the problem and makes it possible to integrate the system of coupled quantum-semiclassical equations with the necessary accuracy and quantitatively describes the processes of atomic-ion collisions in hybrid traps, including resonance effects.
In the development of atomic, molecular, and optical (AMO) physics, atom-ion hybrid systems are characterized by the presence of a new tool in the experimental AMO toolbox: atom-ion interactions. One of the main limitations in state-of-the-art atom-ion experiments is represented by the micromotion component of the ions’ dynamics in a Paul trap, as the presence of micromotion in atom-ion collisions results in a heating mechanism that prevents atom-ion mixtures from undergoing a coherent evolution. Here, we report the design and the simulation of a novel ion trapping setup especially conceived of for integration with an ultracold atoms experiment. The ion confinement is realized by using an electro-optical trap based on the combination of an optical and an electrostatic field, so that no micromotion component will be present in the ions’ dynamics. The confining optical field is generated by a deep optical lattice created at the crossing of a bow-tie cavity, while a static electric quadrupole ensures the ions’ confinement in the plane orthogonal to the optical lattice. The setup is also equipped with a Paul trap for cooling the ions produced by photoionization of a hot atomic beam, and the design of the two ion traps facilitates the swapping of the ions from the Paul trap to the electro-optical trap.
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.
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.
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.