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arXiv:1510.03985 · Physical Review A

Superstatistical velocity distributions of cold trapped ions in molecular-dynamics simulations

I. Rouse, Stefan Willitsch

Published Nov 19, 2015• 18 citations
arXivHTMLPDF

Abstract

We present a realistic molecular-dynamics treatment of laser-cooled ions in radio-frequency ion traps which avoids previously made simplifications such as modeling laser cooling as a friction force and combining individual heating mechanisms into a single effective heating force. Based on this implementation, we show that infrequent energetic collisions of single ions with background gas molecules lead to pronounced heating of the entire ion ensemble and a time-varying secular ensemble temperature, which manifests itself in a superstatistical time-averaged velocity distribution of the ions. The effect of this finding on the experimental determination of ion temperatures and rate constants for cold chemical reactions is discussed.

DOI
10.1103/physreva.92.053420

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We present a realistic molecular-dynamics treatment of laser-cooled ions in radio-frequency ion traps which avoids previously made simplifications such as modeling laser cooling as a friction force and combining individual heating mechanisms into a single effective heating force. Based on this implementation, we show that infrequent energetic collisions of single ions with background gas molecules lead to pronounced heating of the entire ion ensemble and a time-varying secular ensemble temperature, which manifests itself in a superstatistical time-averaged velocity distribution of the ions. The effect of this finding on the experimental determination of ion temperatures and rate constants for cold chemical reactions is discussed.
The properties of cold ion plasmas with large numbers (>200)(>200)(>200) of laser- and sympathetically cooled species are modeled in detail using molecular dynamics simulations. We describe how to extract temperatures and ion numbers from CCD images. The identification of the ion species by excitation of their oscillation modes is discussed. The sympathetic cooling efficiency, effects of the rf micromotion and of collision heating by a neutral background gas are analyzed, in part experimentally.
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.
The nonlinear dynamics of large ion clouds ($N\ensuremath{\ge}256$ ions) trapped in radio-frequency (rf) traps and coupled to laser cooling give rise to a bistable behavior of the temperature. Numerical simulations of the free evolution of a large three-dimensional spherical cloud is used to characterize how the oscillating field amplitude and the ion number control the rf-heating rate and the switching between the two stable states. We show that the heating rate does not significantly depend on the ion number but strongly depends on the oscillating field. This exhibits the major role played by the density of the ensemble. The competition between the radio-frequency heating and the laser cooling is also discussed. They are used to design scenarios to take advantage of the threshold effect to detect and quantify perturbations by an intruder.
Trapping molecular ions that have been sympathetically cooled with laser-cooled atomic ions is a useful platform for exploring cold ion chemistry. We designed and characterized a new experimental apparatus for probing chemical reaction dynamics between molecular cations and neutral radicals at temperatures below 1 K. The ions are trapped in a linear quadrupole radio-frequency trap and sympathetically cooled by co-trapped, laser-cooled, atomic ions. The ion trap is coupled to a time-of-flight mass spectrometer to readily identify product ion species and to accurately determine trapped ion numbers. We discuss, and present in detail, the design of this ion trap time-of-flight mass spectrometer and the electronics required for driving the trap and mass spectrometer. Furthermore, we measure the performance of this system, which yields mass resolutions of m/Δm ≥ 1100 over a wide mass range, and discuss its relevance for future measurements in chemical reaction kinetics and dynamics.
The problem for molecular identification knows many solutions, which include mass spectrometers whose mass sensitivity depends on the performance of the detector involved. The purpose of this article is to show by means of molecular dynamics simulations how a laser-cooled ion cloud, confined in a linear radio-frequency trap, can reach the ultimate sensitivity providing the detection of individual charged heavy molecular ions. In our simulations, we model the laser-cooled Ca+ ions as two-level atoms, confined thanks to a set of constant and time oscillating electrical fields. A singly charged molecular ion with a mass of 106 amu is propelled through the ion cloud. The induced change in the fluorescence rate of the latter is used as the detection signal. We show that this signal is due to a significant temperature variation triggered by the Coulomb repulsion and amplified by the radio-frequency heating induced by the trap itself. We identify the optimum initial energy for the molecular ion to be detected, and furthermore, we characterize the performance of the detector for a large range of confinement voltages.