Characterization of ion Coulomb crystals in a linear Paul trap

Abstract

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 mediumsized 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.

Sympathetic crystallization of CaH+produced by a laser-induced reaction

“…The detailed description of our experimental setup is described in a previous paper [10,11]. Here we present a brief summary of the present improved setup.…”

“…On one hand, for large Ca + Coulomb crystals with an ion number of more than N > 2000 ions, the ion number density n q at 0 K in a linear Paul trap was calculated [10]. The number of Ca + ions is determined by the product of n q and the volume of a Coulomb crystal which can be determined from the size of a fluorescence image.…”

“…We successfully produced CaH + and observed the sympathetic crystallization. The characterization of two-species Coulomb crystals was performed by comparing experimental fluorescence images to calculated crystal images using molecular dynamics simulations [10]. Finally, the reaction rates of the laser-induced reaction were measured under typical experimental conditions and the reaction rate coefficient for room temperature was deduced.…”

Shape and strength of dynamical couplings between vibrational levels of the H2 +, HD+ and D2 + molecular ions in collision with He as a buffer gas

“…The ions exchange kinetic energy by elastic collisions which is removed by laser cooling of the atomic species. Due to the long range Coulomb interaction, the sympathetic cooling technique turns out to be efficient in the translational cooling while leaving the molecular ions internally hot [3,4].…”

\(\bar{\text{H}}^{+}\) Sympathetic Cooling Simulations with a Variable Time Step

“…We therefore have a low density mesoscopic system which would be poorly described by mean-field methods so we cannot use NlogN approximate methods [17] for the Coulomb interaction and we have to exactly compute it using the N 2 all-pairs approach. We solve Newton's equations including the time-dependent confinement electric fields of the linear trap, the exact Coulomb force between all ion pairs and the laser interaction [18][19][20][21][22][23].…”