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Physical Review A

Molecular-dynamics simulations of cold single-species and multispecies ion ensembles in a linear Paul trap

C. B. Zhang, David Offenberg, Bernhard Roth, M. A. Wilson, Stephan Schiller

Published Jul 30, 2007• 105 citations
Publisher

Abstract

The properties of cold ion plasmas with large numbers $(>200)$ 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.

DOI
10.1103/physreva.76.012719

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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.
We investigate the coupling between motional resonances of translationally cold (10mK10\phantom{\rule{0.3em}{0ex}}\mathrm{mK}10mK range) atomic and molecular ions in multispecies Coulomb crystals, stored in a linear Paul trap. The atomic and molecular ions were sympathetically cooled by laser-cooled Be+{\mathrm{Be}}^{+}Be+ ions. The motional resonances of the different ion species were determined nondestructively with high mass-to-charge resolution upon excitation with an oscillating electric field. The experimental results show good agreement with results from molecular dynamics simulations and allow for a precise identification of sympathetically cooled particles in multispecies ion crystals.
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.
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.
An investigation of the sympathetic cooling \nmethod for the studies of large ultra-cold molecular ions in a quadrupole ion trap has been conducted.Molecular dynamics simulations are performed to study the rf heating mechanisms in the ion trap. The dependence of \nrf heating rates on the ion temperature, trapping parameters, \nand the number of ions is obtained. New rf heating mechanism \naffecting ultra-cold ion clouds exposed to laser radiation is described.The saturation spectroscopy setup of the hyperfine spectra \nof the molecular iodine has been built to provide an accurate frequency reference for the laser wavelength. This reference is used to obtain the fluorescence lineshapes of \nthe laser cooled Mg+^++ ions under different trapping conditions.The ion temperatures are deduced from the measurements, and \nthe influence of the rf heating rates on the fluorescence lineshapes \nis also discussed. Cooling of the heavy (m=720m=720m=720a.u.) fullerene ions to under 10K by the means of the sympathetic cooling by the Mg+^++ ions(m=24m=24m=24a.u.) is demonstrated. The single-photon imaging system has been developed and used to obtain the images of the Mg+^++ ion crystal structures at mK temperatures.
We have created multispecies Coulomb crystals in a linear Paul trap containing up to a few hundred ions of which more than 5050%50 were cooled only sympathetically through the Coulomb interaction with laser-cooled Mg+{\mathrm{Mg}}^{+}Mg+ ions. In an extreme case, one laser-cooled ion maintained order in a 15 ion string. Ion species segregation was obtained by radiation pressure. Previous experiments and molecular dynamics simulations suggest the temperature is 10 mK or lower. These results indicate that a wide range of atomic and molecular ions can be cooled and localized in linear Paul traps which is important for improvements in spectroscopic studies of such ions.
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.