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arXiv:2203.05196

Individual qubit addressing of rotating ion crystals in a Penning trap

Anthony Polloreno, Ana María Rey, J. J. Bollinger

Published Mar 10, 2022• 0 citations
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Abstract

Trapped ions boast long coherence times and excellent gate fidelities, making them a useful platform for quantum information processing. Scaling to larger numbers of ion qubits in RF Paul traps demands great effort. Another technique for trapping ions is via a Penning trap where a 2D crystal of hundreds of ions is formed by controlling the rotation of the ions in the presence of a strong magnetic field. However, the rotation of the ion crystal makes single ion addressability a significant challenge. We propose a protocol that takes advantage of a deformable mirror to introduce AC Stark shift patterns that are static in the rotating frame of the crystal. Through numerical simulations we validate the potential of this protocol to perform high-fidelity single-ion gates in crystalline arrays of hundreds of ions.

DOI
10.48550/arxiv.2203.05196

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Trapped ions boast long coherence times and excellent gate fidelities, making them a useful platform for quantum information processing. Scaling to larger numbers of ion qubits in RF Paul traps demands great effort. Another technique for trapping ions is via a Penning trap where a 2D crystal of hundreds of ions is formed by controlling the rotation of the ions in the presence of a strong magnetic field. However, the rotation of the ion crystal makes single ion addressability a significant challenge. We propose a protocol that takes advantage of a deformable mirror to introduce AC Stark shift patterns that are static in the rotating frame of the crystal. Through numerical simulations we validate the potential of this protocol to perform high-fidelity single-ion gates in crystalline arrays of hundreds of ions.
Trapped ions boast long coherence times and excellent gate fidelities, making them a useful platform for quantum information processing. Penning traps offer the possibility of trapping large two-dimensional crystals of several hundred ions. The ions are confined by controlling the rotation of the ion crystal in the presence of a strong magnetic field. However, the rotation of the ion crystal makes single ion addressability a significant challenge. We propose a protocol that takes advantage of a deformable mirror to introduce AC Stark shift patterns that are static in the rotating frame of the crystal. Through numerical simulations we validate the potential of this protocol to perform high-fidelity single-ion gates in crystalline arrays of hundreds of ions.
Penning ion traps as quantum platforms have primarily utilized global control and symmetric Dicke states for quantum simulation and sensing experiments. The introduction of local control greatly increases the power of the platform as a quantum simulator but is technically challenging due to the rapid rotation of the ion crystals. Here we use an ultraviolet-compatible spatial light modulator (SLM) to imprint programmable AC Stark shift patterns with different azimuthal symmetries and gradients that co-rotate with the ion crystals, demonstrating localized coherent control of single plane crystals with greater than 100 ions. Comparisons of the measured ion qubit populations with calculations from independent measurements of the applied AC Stark shift patterns show good agreement, validating the technique and providing a path, with a higher format SLM, for parallelizable, coherent individual ion addressing in Penning traps.
We implement individual addressing and readout of ions in a rigidly rotating planar crystal in a compact, permanent magnet Penning trap. The crystal of ^{40}Ca^{+} is trapped and stabilized without defects via a rotating triangular potential. The trapped ion fluorescence is detected in the rotating frame for parallel readout. The qubit is encoded in the metastable D_{5/2} manifold enabling the use of high-power near-infrared laser systems for qubit operations. Addressed σ_{z} operations are realized with a focused ac Stark shifting laser beam. We demonstrate addressing of ions near the center of the crystal and at large radii. Simulations show that the current addressing operation fidelity is limited to ∼97% by the ion's thermal extent for the in-plane modes near the Doppler limit, but this could be improved to infidelities <10^{-3} with sub-Doppler cooling. The techniques demonstrated in this Letter complete the set of operations for quantum simulation with the platform.
Large ion crystals in Penning traps provide a platform for quantum simulation and sensing with hundreds of spins, but their continuous rigid-body rotation has so far limited flexible local qubit control. Here we demonstrate programmable coherent site-selective spin control across large rotating 9Be+{}^{9}\mathrm{Be}^{+}9Be+ crystals in a Penning trap. A tightly focused off-resonant laser beam drives local RzR_zRz​ phase rotations via differential AC Stark shifts. Beam steering synchronised with crystal rotation enables addressing of arbitrary ions throughout the crystal. Ramsey-based characterisation shows Rz(π)R_z(π)Rz​(π) gate fidelity of 0.950(4) and nearest-neighbour crosstalk error of 0.021(6). We demonstrate preparing spatially structured spin patterns, generating a biskyrmion spin texture in a single-layer crystal, and then extend the method to bilayer crystals where we perform layer-selective addressing operations. We further demonstrate dual-quadrature Ramsey sensing by imprinting a relative π/2π/2π/2 phase shift between spatial sub-ensembles, enabling simultaneous measurement of orthogonal spin components within a single experimental realisation. These results establish programmable local control in large rotating ion crystals, opening new routes for engineering spatially structured quantum states in multidimensional trapped-ion systems.
We provide an introduction to the use of ion crystals in a Penning trap for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser Doppler cooled, and the mutual Coulomb repulsion of the ions leads to the formation of crystalline arrays. The structure and dimensionality of the resulting ion crystals may be tuned using a combination of control laser beams and external potentials. We discuss the use of two-dimensional 9^{9}9Be+^{+}+ ion crystals for experimental tests of quantum control techniques. Our primary qubit is the 124 GHz ground-state electron spin flip transition, which we drive using microwaves. An ion crystal represents a spatial ensemble of qubits, but the effects of inhomogeneities across a typical crystal are small, and as such we treat the ensemble as a single effective spin. We are able to initialize the qubits in a simple state and perform a projective measurement on the system. We demonstrate full control of the qubit Bloch vector, performing arbitrary high-fidelity rotations ($\tau_{\pi}\sim$200 μ\muμs). Randomized Benchmarking demonstrates an error per gate (a Pauli-randomized π/2\pi/2π/2 and π\piπ pulse pair) of 8±1×10−48\pm1\times10^{-4}8±1×10−4. Ramsey interferometry and spin-locking measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical free-induction decay coherence time of $T_{2}\sim$2 ms, and a limiting $T_{1\rho}\sim$688 ms. These experimental specifications make ion crystals in a Penning trap ideal candidates for novel experiments in quantum control. As such, we briefly describe recent efforts aimed at studying the error-suppressing capabilities of dynamical decoupling pulse sequences, demonstrating an ability to extend qubit coherence and suppress phase errors. We conclude with a discussion of future avenues for experimental exploration, including the use of additional nuclear-spin-flip transitions for effective multiqubit protocols, and the potential for Coulomb crystals to form a useful testbed for studies of large-scale entanglement.
Two-dimensional (2D) ion crystals may represent a promising path to scale up qubit numbers for ion trap quantum information processing. However, to realize universal quantum computing in this system, individually addressed high-fidelity two-qubit entangling gates still remain challenging due to the inevitable micromotion of ions in a 2D crystal as well as the technical difficulty in 2D addressing. Here we demonstrate two-qubit entangling gates between any ion pairs in a 2D crystal of four ions. We use symmetrically placed crossed acousto-optic deflectors (AODs) to drive Raman transitions and achieve an addressing crosstalk error below 0.1%. We design and demonstrate a gate sequence by alternatingly addressing two target ions, making it compatible with any single-ion addressing techniques without crosstalk from multiple addressing beams. We further examine the gate performance versus the micromotion amplitude of the ions and show that its effect can be compensated by a recalibration of the laser intensity without degrading the gate fidelity. Our work paves the way for ion trap quantum computing with hundreds to thousands of qubits on a 2D ion crystal. Quantum gates in 2D ion crystals are more challenging than in 1D. Here, the authors use their 2D ion trap platform and acousto-optical deflectors to demonstrate a 2-qubit gate that can stand the ion micromotion in such configuration.