Ions in coulomb crystals are sufficiently cooled and well isolated from the environment, which makes them an ideal platform for the research of high precision spectroscopy. Ion coulomb crystals (ICC) constituted by multispecies ions can provide important information about the nucleus, such as isotope shifts and hyperfine splittings. In order to extract the spectroscopic data with a high precision, the status of ICC needs to be properly evaluated. In this paper, we utilize the molecular dynamics simulation software LAMMPS and the (py) Lion package to simulate the dynamics of ICC with multispecies ions. To make a better comparison between the simulation results and experimental observations, we propose an ICC tomography scheme with the fluorescence light-sheet microscopy. This work can be applied to make better estimation on dynamic parameters of both laser cooled and sympathetically cooled ions.

Coulomb crystal yields a wide range of applications including quantum computing and simulation, phase transitions, quantum logic spectroscopy, nonlinear dynamics and chaos, chemical reaction process, etc. The structure of the Coulomb crystal and the trajectory of each trapped ion are typically determined by the parameters of the trap and the ion species. However, dark ions are often inevitable in experiments, which introduces uncertainty to the desired crystal structures and ion trajectories. Few research has been conducted to investigate the configuration change of the crystal in the presence of dark ions and the influence of a dark ion on its surrounding ion trajectories in a multi-ion system. In this paper, we utilize the molecular dynamics simulation software LAMMPS and the (py)Lion package (modified to adapt the semi-classical theory of laser cooling) for the simulation of the 3D ion trajectories of Coulomb crystals. The formation process of ⁴⁰Ca⁺ Coulomb crystals in a linear trap is simulated. With the micromotion and secular motion trajectories of each ion, we calculate the temperature of Coulomb crystal and the average velocity of specific ions. It’s observed that the crystal structure exhibits obvious layering phenomenon when the trapped ions yield a large difference in their charge-to-mass ratio (CMR), however, layering is not obvious with a small difference in the CMR. In addition, we simulate and compare the Coulomb crystal structure formed by pure ⁴⁰Ca⁺ ions and that formed by ⁴⁰Ca⁺ ions mixed with a small number of dark ions including isotopic ions (⁴⁴Ca⁺) and impurity ions (CaH⁺). Three different cases are investigated, namely the 1D ion string, 2D plane structure and 3D helical structure. Results show that ions in the neighborhood of a dark ion exhibit around micron-order position changes compared to their positions before the dark ion is formed. Such a change can be measured in experiment through microscopic imaging, providing a way to identify dark ions in Column crystals with a large number of ions.

Coulomb crystal yields a wide range of applications including quantum computing and simulation, phase transitions, quantum logic spectroscopy, nonlinear dynamics and chaos, chemical reaction process, etc. The structure of the Coulomb crystal and the trajectory of each trapped ion are typically determined by the parameters of the trap and the ion species. However, dark ions are often inevitable in experiments, which introduces uncertainty to the desired crystal structures and ion trajectories. Few research has been conducted to investigate the configuration change of the crystal in the presence of dark ions and the influence of a dark ion on its surrounding ion trajectories in a multi-ion system. In this paper, we utilize the molecular dynamics simulation software LAMMPS and the (py) Lion package (modified to adapt the semi-classical theory of laser cooling) for the simulation of the 3D ion trajectories of Coulomb crystals. The formation process of ⁴⁰Ca⁺Coulomb crystals in a linear trap is simulated. With the micromotion and secular motion trajectories of each ion, we calculate the temperature of Coulomb crystal and the average velocity of specific ions. It’s observed that the crystal structure exhibits obvious layering phenomenon when the trapped ions yield a large difference in their charge-to-mass ratio (CMR), however, layering is not obvious with a small difference in the CMR. In addition, we simulate and compare the Coulomb crystal structure formed by pure ⁴⁰Ca⁺ ions and that formed by ⁴⁰Ca⁺ ions mixed with a small number of dark ions including isotopic ions (⁴⁴Ca⁺) and impurity ions (CaH⁺). Three different cases are investigated, namely the 1D ion string, 2D plane structure and 3D helical structure. Results show that ions in the neighborhood of a dark ion exhibit around micron-order position changes compared to their positions before the dark ion is formed. Such a change can be measured in experiment through microscopic imaging, providing a way to identify dark ions in Column crystals with a large number of ions.