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Optical Manipulation and Structured Materials Conference (OMC)

One-dimensional radial Coulomb crystals in a quadrupole Paul trap

Anna V. Romanova, Semyon S. Rudyi, Yu. Rozhdestvensky

Published Sep 20, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.3008336

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Acta Physica Sinica•Sep 29, 2022•1 citation
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.
Through finite-element simulation, the axial potential distribution of the ion trap is analyzed. The effects of the central hole diameter of the end cap and the spacing between the two end caps on the axial geometric parameters of the ion trap are investigated. Based on these findings, a set of linear Paul traps is designed by selecting suitable end caps and quadrupoles. Stable trapping of calcium ions (Ca+) is successfully achieved, and these ions are subsequently laser-cooled into ionic Coulomb crystals. In the experiment, secular motion excitation of the Ca+ ion Coulomb crystal is performed, yielding an axial geometric parameter of 0.115(1) for the ion trap. This value aligns well with the simulation result of 0.114(2). The precise determination of the axial geometric parameter provides a solid foundation for subsequent high-precision optical or mass spectrometry measurements.
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.
Ion Coulomb crystals of laser-cooled Ca+{\text{Ca}}^{+}Ca+ ions have been observed in a cryogenic linear octupole rf ion trap for the first time. Due to the almost field-free central region, large ion crystals containing over 104{10}^{4}104 ions of millimeter size were successfully produced. The shapes of the crystals can be manipulated by changing the static voltages applied to the octupole rods and the endcap electrodes. Quasi-two-dimensional Coulomb crystals consisting of a small number of ions were also observed with single-ion sensitivity. When a large number of ions is crystallized in the octupole trap, a new kind crystal image with a dip along the axial direction was obtained. The results show that a linear octupole trap and multipole traps are available for producing large, cold, and novel ion Coulomb crystals. The planar ring-type crystal which has not been observed before may lead to future interesting applications.
We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.
We report on the observations of three-dimensional long-range ordered structures in the central 40^{40}40Ca+^++ ion component of 40^{40}40Ca+^++--44^{44}44Ca+^++ two-species ion Coulomb crystals in a linear Paul trap. In contrast to long-range ordering previously observed in single species crystals, the structures observed are strikingly persistent and always of one specific type in one particular orientation. Molecular dynamics simulations strongly indicate that these characteristics are a hitherto unpredicted consequence of the co-axial cylindrical symmetry of the central ion component of the Coulomb crystal and the radio frequency quadrupole trapping field.
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.