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Chinese Physics B

Determining the structural phase transition point from the temperature of 40 Ca + Coulomb crystal

Ting Chen, Lijun Du, Hong-Fang Song, Peiliang Liu, Yao Ting Huang, Xin Tong, Hua Guan, Kelin Gao

Published Nov 28, 2014• 5 citations
Publisher

Abstract

We observed the linear-to-zigzag structural phase transition of a Ca-40(+) crystal in a homemade linear Paul trap. The values of the total temperature of the ion crystals during the phase transition are derived using the molecular-dynamics (MD) simulation method. A series of simulations revealed that the ratio of the radial to axial secular frequencies has a dependence on the total temperature that obeys different functional forms for linear and zigzag structures, and the transition point occurs where these functions intersect; thus, the critical value of the ratio of secular frequencies that drives the structure phase transition can be derived.

DOI
10.1088/1674-1056/23/12/123702

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We observed the linear-to-zigzag structural phase transition of a Ca-40(+) crystal in a homemade linear Paul trap. The values of the total temperature of the ion crystals during the phase transition are derived using the molecular-dynamics (MD) simulation method. A series of simulations revealed that the ratio of the radial to axial secular frequencies has a dependence on the total temperature that obeys different functional forms for linear and zigzag structures, and the transition point occurs where these functions intersect; thus, the critical value of the ratio of secular frequencies that drives the structure phase transition can be derived.
We observed the linear-to-zigzag structural phase transition of a40Ca+crystal in a homemade linear Paul trap. The values of the total temperature of the ion crystals during the phase transition are derived using the molecular-dynamics(MD) simulation method. A series of simulations revealed that the ratio of the radial to axial secular frequencies has a dependence on the total temperature that obeys different functional forms for linear and zigzag structures, and the transition point occurs where these functions intersect; thus, the critical value of the ratio of secular frequencies that drives the structure phase transition can be derived.
Abstract We investigate the structural transitions of ion Coulomb crystals (ICCs) using molecular dynamics simulations, focusing on the effects of ion number and the anisotropy of the confining potential. Our simulations reveal transitions from linear to zigzag to shell formation and dissolution to a two-dimensional plane finally. We characterized the phase transition points, the number of phase transitions. This study provides a more detailed analysis than previous works and establishes a power-law relationship between the critical anisotropy parameter and ion number. Our results offer valuable insights for the precise determination of ICC structure, trapped ion counting, and trapping potential parameters in experimental settings.
We have observed crystalline structures formed by laser cooled Ca + ions in a three-dimensional confining potential. The potential has been realized using a linear Paul trap with different ratios of potential strength in the axial and radial directions. For radial confining potentials stronger than the axial potential, we find linear structures with a continuous transition from strings to helices with decreasing potential asymmetry. When a quasi-two-dimensional potential is formed we observe ring structures with a given maximum ion number per ring which we followed up to 19. The observations are essentially in agreement with molecular dynamics calculations in static two-dimensional potentials.
Coulomb crystals have applications in many areas such as quantum computing and simulation, quantum logic spectroscopy, nonlinear dynamics and chaos, phase transitions, and chemical reaction process. 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 experiment, which introduces uncertainty into the desired crystal structures and ion trajectories. Few researches have 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 work, we utilize the molecular dynamics simulation software LAMMPS and the (py)LIon package (modified to adapt the semi-classical theory of laser cooling) for simulating the three-dimensional ion trajectories of Coulomb crystals. The formation process of 40Ca+ Coulomb crystal 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 is 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 with 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 one-dimensional ion string, two-dimensional planar structure and three-dimensional helical structure. The results show that the ions in the neighborhood of a dark ion exhibit around micron-order position change compared with their positions before the dark ion is formed. Such a change can be measured in experiment through microscopic imaging, thereby providing a way to identify the formation of dark ions in Column crystals with a large ion number.
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.
In this work, we have studied the dynamics of 7-ions Ca+ Coulomb crystal in a linear quadrupole trap with flat end-cap electrodes. We have introduced geometrical parameters to determine points of phase transitions in the crystal. Then we have numerically calculated a phase diagram for this case and simulated the corresponding Coulomb crystals. It was shown that new one-dimensional radial Coulomb crystals are observed with the application of both high end-cap voltage (more than 1200 V) and a bias voltage on linear electrodes.