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Mode shaping in mixed ion crystals of 40Ca2+ and 40Ca+

Thomas Feldker, Lennart Pelzer, P. Bachor, Ruth Steinborn, Daniel Kolbe, J. Walz, Ferdinand Schmidt‐Kaler

Published Jan 1, 2014• 6 citations
OpenAlex

Abstract

We present studies of mixed Coulomb crystals of 40Ca+ and 40Ca2+ ions in a linear Paul trap. Doubly charged ions are produced by photoionisation of trapped 40Ca+ with a vacuum ultraviolet laser source and sympathet-ically cooled via Doppler cooled 40Ca+ ions. We in-vestigate experimentally and theoretically the struc-tural configurations and the vibrational modes of these mixed crystals. Our results with 40Ca2+ are an impor-tant step towards experimental realization of the pro-posals for mode shaping in a linear crystal and spin-dependent configuration changes from zigzag to linear as proposed by Li et al., Phys. Rev. A 87, (2013) 052304 and Phys. Rev. Lett 108, (2012) 023003 using ions excited to Rydberg states. 1

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We present studies of mixed Coulomb crystals of 40Ca+ and 40Ca2+ ions in a linear Paul trap. Doubly charged ions are produced by photoionisation of trapped 40Ca+ with a vacuum ultraviolet laser source and sympathet-ically cooled via Doppler cooled 40Ca+ ions. We in-vestigate experimentally and theoretically the struc-tural configurations and the vibrational modes of these mixed crystals. Our results with 40Ca2+ are an impor-tant step towards experimental realization of the pro-posals for mode shaping in a linear crystal and spin-dependent configuration changes from zigzag to linear as proposed by Li et al., Phys. Rev. A 87, (2013) 052304 and Phys. Rev. Lett 108, (2012) 023003 using ions excited to Rydberg states. 1
We report on structural properties of two-component Coulomb crystals in a linear Paul trap. The crystals consist of two laser cooled ion species, 24Mg+ and 40Ca+. The lighter 24Mg+ ions form an inner cylindrical crystal structure surprisingly similar to that of an infinitely long single component crystal, while the outermost shell of the surrounding 40Ca+ ions have a spheroidal shape, which is highly insensitive to the presence of the 24Mg+ ions. Observed changes in the radial separation of the two ion species with the radius of the inner cylindrical crystal is explained by a simple model.
We obtain bi-component Coulomb crystals using laser-cooled 40Ca+ ions to sympathetically cool 9Be+ ions in a linear Paul trap. The shell structures of the bi-component Coulomb crystals are investigated. The secular motion frequencies of the two different ions are determined and compared with those in the single-component Coulomb crystals. In the radial direction, the resonant motion frequencies of the two ionic species shift toward each other due to the strong motion coupling in the ion trap. In the axial direction, the motion frequency of the laser-cooled 40Ca+ is impervious to the sympathetically cooled 9Be+ ions because the spatially separation of the two different ionic species leads to the weak motion coupling in the axial direction.
44Ca+, Zn+, or Ga+ ions are sympathetically cooled by Coulomb interaction with laser-cooled 40Ca+ ions, and motional resonances of these ions are observed by monitoring the fluorescence of the 40Ca+ ions. In the experiment of sympathetic cooling of 44Ca+, the ratio of the decrease in the fluorescence signal at the motional resonance of the sympathetically cooled species to that at the motional resonance of the laser-cooled species is almost proportional to the number ratio of the two species. In the case of Ga+ ions as the sympathetically cooled species, the change in the response of sympathetically cooled species becomes larger as the temperature of the ion cloud decreases. Crystallization of an ion cloud which contains both 40Ca+ and Zn+ (or Ga+) is observed.
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.
We report on the sympathetic cooling and Coulomb crystallization of xenon highly charged ions (HCIs) with laser-cooled Ca+^++ ions. The HCIs are produced in a compact electron beam ion trap, then charge selected, decelerated, and finally injected into a cryogenic linear Paul trap. There, they are captured into 40^{40}40Ca+^++ Coulomb crystals, and co-crystallized within them, causing dark voids in their fluorescence images. Fine control over the number of trapped ions and HCIs allows us to realize mixed-species crystals with arbitrary ordering patterns. By investigating Xeq+^{q+}q+--Ca+^++ strings, we confirm the HCI charge states, measure their lifetime and characterize the mixed-species motional modes. Our system effectively combines the established quantum control toolbox for Ca+^++ with the rich set of atomic properties of Xe highly charged ions, providing a resourceful platform for optical frequency metrology, searches for signatures of new physics, and quantum information science.