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Improving Molecular Dynamics Simulations of Ion Coulomb Crystals in Linear Paul Traps

Kevin M Loeffler

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

Molecular dynamics simulations of ion Coulomb crystals in linear Paul traps allow for the extraction of properties such as ion temperature and ion counts enabling the investigation of ion chemistry in the ultra-cold regime. These simulations reproduce experimental CCD images using density plots of simulated ions allowing for comparisons to be drawn between simulated and experimental results and providing information inaccessible to the researcher, such as the locations of clouds of non- uorescing species. In this thesis, a method for creating these simulated CCD images is presented, as well as the demonstration of a fourth order integrator for producing more accurate calculations of the ion energy. The simulation of a single frequency Paul trap is presented and the ability to match simulations with experimental parameters as inputs to experimental results is demonstrated in order to show that the simulations that have been constructed can be used to analyze experimental data and work as a predictive lab tool for future explorations of ultra-cold chemistry.

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Structural and energetic properties of molecular Coulomb crystals in a surface-electrode ion trap

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Cold molecular ions are of great interest for applications in cold collision studies, chemistry, precision spectroscopy and quantum technologies. In this context, sympathetic cooling of molecular ions by the interaction with laser-cooled atomic ions is a powerful method to cool their translational motion and achieve translational temperatures in the millikelvin range. Recently, we implemented this method in a surface-electrode ion trap. The flexibility in shaping the trapping potentials offered by the surface-electrode structure enabled us to generate planar bicomponent Coulomb crystals and spatially separate the molecular from the atomic ions. Here, we present a detailed description of the fabrication and simulation of the trap as well as a theoretical and experimental investigation of the structural and energetic properties of the Coulomb crystals obtained in the device. We discuss in more detail the separation of different ion species using static electric fields and explore the effects of trap anharmoncities on the shape of bicomponent crystals.

New Journal of Physics•Apr 16, 2015•8 citations
Molecular dynamics simulations of ion Coulomb crystals in linear Paul traps allow for the extraction of properties such as ion temperature and ion counts enabling the investigation of ion chemistry in the ultra-cold regime. These simulations reproduce experimental CCD images using density plots of simulated ions allowing for comparisons to be drawn between simulated and experimental results and providing information inaccessible to the researcher, such as the locations of clouds of non- uorescing species. In this thesis, a method for creating these simulated CCD images is presented, as well as the demonstration of a fourth order integrator for producing more accurate calculations of the ion energy. The simulation of a single frequency Paul trap is presented and the ability to match simulations with experimental parameters as inputs to experimental results is demonstrated in order to show that the simulations that have been constructed can be used to analyze experimental data and work as a predictive lab tool for future explorations of ultra-cold chemistry.
We describe a simple and fast method for simulating observed images of ion Coulomb crystals. In doing so, cold elastic collisions between Coulomb crystals and virtual very light atoms are implemented in a molecular dynamics (MD) simulation code. Such an approach reproduces the observed images of Coulomb crystals by obtaining density plots of the statistics of existence of each ion. The simple method has the advantage of short computing time in comparison with previous calculation methods. As a demonstration of the simulation, the formation of a planar Coulomb crystal with a small number of ions has been investigated in detail in a linear ion trap both experimentally and by simulation. However, also large Coulomb crystals including up to 1400 ions have been photographed and simulated to extract the secular temperature and the number of ions. For medium-sized crystals, a comparison between experiments and calculations has been performed. Moreover, an MD simulation of the sympathetic cooling of small molecular ions was performed in order to test the possibility of extracting the temperature and the number of refrigerated molecular ions from crystal images of laser-cooled ions. Such information is basic to studying ultracold ion-molecule reactions using ion Coulomb crystals including sympathetically cooled molecular ions.
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.
This thesis describes the study of a range of ion-molecule reactions at very low collision energies using a newly developed experimental technique which involves the reaction of velocity-selected beams of translationally cold neutral molecules with very low kinetic energy ion ensembles. These studies have been enabled by the construction of a new apparatus for trapping and laser-cooling gas phase atomic ions (40Ca⁺). The laser-cooling process results in the formation of ordered, low kinetic energy, lattice-like ion structures, also known as "Coulomb crystals". The properties of single and multicomponent Coulomb crystals (which may also involve molecular ions), and their manipulation via modulation of the applied fields, are explored experimentally and with the use of molecular dynamics simulations. Variations in the laser-cooling parameters are shown to result in different steady-state populations of the electronic states of 40Ca⁺ involved with the laser cooling cycle, and these are modelled within an appropriate theoretical framework. The imaging of 40Ca⁺ fluorescence as a function of time allows the study of various ion-molecule reactions at collision energies around 300 K, with single ion sensitivity. These reaction studies are extended to low-temperature (collision energies close to 1 K), by combination of the ion trap apparatus with a bent quadrupole guide velocity-selector. Ion-molecule collision energies are shown to be variable over a short range through a change in the quadrupole guide voltage, or the ion trapping parameters; the effect of these modulations on the rate constant is explored for Ca⁺ + CH₃F. Bimolecular rate constants for the reactions of 40Ca⁺ with CH₃F, CH₂F₂ and CH₃Cl have been determined for a range of 40Ca⁺ state populations, allowing resolution of the global rate contributions from the ground and combined excited states. These results are analysed in the context of capture theories and ab initio electronic structure calculations. In each case, suppression of the ground state rate constant is explained by the presence of either a submerged or real barrier on the ground state potential surface. Rates of reaction from the combined excited states are generally found to be in line with capture theories, and in some cases variation is found between the high and low collision energy regimes. Molecular product ions generated in these experiments have been shown to be sympathetically-cooled into the crystal structure, and subsequently identified through resonance-excitation mass spectrometry. Molecular ions were also produced by multiphoton laser ionisation of a thermal background gas of OCS molecules. An ion-molecule reaction involving a molecular ion, that of charge transfer between OCS⁺ and ND₃, has been studied at a collision energy near 1 K for the first time using sympathetically-cooled OCS⁺ and velocity-selected ND₃. These experiments illustrate the generality of the techniques described herein, and should lead to many possibilities for future studies.
The quadrupole linear Paul trap is one of the key instruments in building highly stable atomic clocks. However, a frequency reference based on a single trapped ion is limited in stability due to the time needed for the interrogation cycle which cannot be further shortened. A promising strategy is the utilization of multiple trapped ions. The ions of the same kind then repulse each other with the Coulomb force, which is countered by the ponderomotive force of the time depended field in the trap. A few ions form a chain along the axis of a linear Paul trap. Adding more ions (a few tens or hundreds) gives rise to Coulomb crystals. We created an efficient simulation code which calculates the motion of such collections of ions in quasi-static radiofrequency fields of real linear quadrupole traps (including the micromotion). We include a model for laser cooling of the ions. The simulation tool can be used to study the formation and the dynamics of Coulomb crystals under conditions corresponding to various experimental setups.
Coulomb crystals, containing up to a few hundred ions of which more than 50% were cooled sympathetically by the Coulomb interaction with laser cooled Mg+ ions, have been produced in a linear Paul trap. By controlling the balance of the radiation pressure from the two cooling lasers, the Coulomb crystals could be segregated according to ion species. Previous studies of ion crystals and molecular dynamics simulations suggest that the temperature may be around 10 mK or lower. The obtained results indicate that a wide range of atomic and molecular ions, which due to their internal structures are not amenable to direct laser cooling, can be effectively cooled and localized (crystallized) in linear Paul traps. For high resolution spectroscopy of such ions this may turn out to be very useful.
Cold molecular ions are of great interest for applications in cold collision studies, chemistry, precision spectroscopy and quantum technologies. In this context, sympathetic cooling of molecular ions by the interaction with laser-cooled atomic ions is a powerful method to cool their translational motion and achieve translational temperatures in the millikelvin range. Recently, we implemented this method in a surface-electrode ion trap. The flexibility in shaping the trapping potentials offered by the surface-electrode structure enabled us to generate planar bicomponent Coulomb crystals and spatially separate the molecular from the atomic ions. Here, we present a detailed description of the fabrication and simulation of the trap as well as a theoretical and experimental investigation of the structural and energetic properties of the Coulomb crystals obtained in the device. We discuss in more detail the separation of different ion species using static electric fields and explore the effects of trap anharmoncities on the shape of bicomponent crystals.