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arXiv:2302.00565 · PRX Quantum

Controlling Two-Dimensional Coulomb Crystals of More Than 100 Ions in a Monolithic Radio-Frequency Trap

Dominik Kiesenhofer, Helene Hainzer, Artem Zhdanov, Philip C. Holz, Matthias Bock, Tuomas Ollikainen, Christian F. Roos

Published Apr 28, 2023• 53 citations
arXivHTMLPDF

Abstract

Linear strings of trapped atomic ions held in radio-frequency (rf) traps constitute one of the leading platforms for quantum simulation experiments, allowing the investigation of interacting quantum matter.However, linear ion strings have drawbacks, such as the difficulty of scaling beyond approximately 50 particles as well as the inability to naturally implement spin models with more than one spatial dimension.Here we present experiments with planar Coulomb crystals of up to 105 40 Ca + ions in a novel monolithic rf trap, laying the groundwork for quantum simulations of two-dimensional spin models with singleparticle control.We characterize the trapping potential by analysis of crystal images and compare the observed crystal configurations with numerical simulations.We further demonstrate stable confinement of large crystals, free of structural configuration changes, and find that rf heating of the crystal is not an obstacle for future quantum simulation experiments.Finally, we prepare the out-of-plane motional modes of planar crystals consisting of up to 105 ions close to their ground state by electromagnetically induced transparency cooling, an important prerequisite for implementing long-range entangling interactions.

DOI
10.1103/prxquantum.4.020317

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Linear strings of trapped atomic ions held in radio-frequency (rf) traps constitute one of the leading platforms for quantum simulation experiments, allowing the investigation of interacting quantum matter.However, linear ion strings have drawbacks, such as the difficulty of scaling beyond approximately 50 particles as well as the inability to naturally implement spin models with more than one spatial dimension.Here we present experiments with planar Coulomb crystals of up to 105 40 Ca + ions in a novel monolithic rf trap, laying the groundwork for quantum simulations of two-dimensional spin models with singleparticle control.We characterize the trapping potential by analysis of crystal images and compare the observed crystal configurations with numerical simulations.We further demonstrate stable confinement of large crystals, free of structural configuration changes, and find that rf heating of the crystal is not an obstacle for future quantum simulation experiments.Finally, we prepare the out-of-plane motional modes of planar crystals consisting of up to 105 ions close to their ground state by electromagnetically induced transparency cooling, an important prerequisite for implementing long-range entangling interactions.
The computational difficulty of solving fully quantum many-body spin problems is a significant obstacle to understanding the behavior of strongly correlated quantum matter. Experimental ion trap quantum simulation is a promising approach for studying these lattice spin models, but has so far been limited to one-dimensional systems. This work argues that such quantum simulation techniques are extendable to a two-dimensional (2D) ion crystal confined in a radio-frequency (rf) trap. Using appropriately chosen parameters, driven ion motion due to the rf fields can be made small and will not limit the types of quantum spin models that can be experimentally encoded. The rf-driven motion is calculated to modestly reduce the stability region of a 2D crystal and must be considered when designing the 2D trap. The system will be scalable to 100+ quantum particles, far beyond the realm of classical intractability, while maintaining the traditional ion trap strengths of individual-ion control, long quantum coherence times, and site-resolved projective spin measurements.
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta.Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task.For many applications, linear chains of ions in conventional traps are ideally suited to address this problem.However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems.Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields.We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal.As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap.Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion.Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one-and two-dimensional crystals.
Large ion crystals in diverse geometries are a key resource for quantum simulation experiments. In this work, we introduce a macroscopic rf trap that supports a wide variety of one-dimensional ion configurations as well as lateral two-dimensional crystals with more than 100 ions. Our design is based on precision-machined fused silica wafers that are stacked to form the trap structure. Ten independently biased electrodes provide flexible control over the axial potential, enabling long one-dimensional crystals, isospaced ion strings, split-well chains, and two-dimensional arrays with tunable aspect ratios. We present the design and fabrication process for this trap and demonstrate the ability to tune the radial secular frequencies, detect and compensate micromotion, rotate the principal axes, and characterize trapped ion heating rates. All trap design and documentation files are freely available alongside this work, to facilitate adoption and further development within the ion trap community.
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.
Laser-cooled atomic ions form ordered structures in radiofrequency ion traps and in Penning traps. Here we demonstrate in a Penning trap the creation and manipulation of a wide variety of ion Coulomb crystals formed from small numbers of ions. The configuration can be changed from a linear string, through intermediate geometries, to a planar structure. The transition from a linear string to a zigzag geometry is observed for the first time in a Penning trap. The conformations of the crystals are set by the applied trap potential and the laser parameters, and agree with simulations. These simulations indicate that the rotation frequency of a small crystal is mainly determined by the laser parameters, independent of the number of ions and the axial confinement strength. This system has potential applications for quantum simulation, quantum information processing and tests of fundamental physics models from quantum field theory to cosmology.