Brian C. Sawyer

We report precision measurements of the ratio of Landé $g$ factors between the $3^2D_{5/2}$ and $4^2S_{1/2}$ states of a single trapped $^{40}\text{Ca}^+$ ion. The measurements are performed in two distinct ion trap apparatus: a cryogenic surface electrode radiofrequency Paul trap and a room-temperature permanent magnet Penning trap. The Penning trap measurements yield a ratio of $0.599~488~813~3(2)$, which represents a more than 40-fold uncertainty reduction compared to previous work. The radiofrequency trap measurement yields a concurring value of $0.599~488~813(6)$. We estimate that systematic shifts for each system are well below the respective statistical uncertainty.

We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a $^{40}$Ca$^+$ ion confined in a compact Penning trap operating with a magnetic field of 0.91 T. Using the same set of laser beams as required for the initial Doppler laser cooling operation, we detune the laser frequencies to produce a narrow two-photon dark resonance. The process achieves a 1/e cooling time constant of 108(8) $μ$s, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800 $μ$s as measured by resonantly probing an electric quadrupole transition near 729 nm. A parametric drive is applied to the trap electrodes which coherently exchanges the axial mode occupation with that of each radial mode, allowing for three-dimensional sub-Doppler cooling using only the axially-propagating laser beams. This sub-Doppler cooling is achieved for an axial oscillation frequency of $ω_z = 2π~\times~$221 kHz, which places the motion well outside of the Lamb Dicke confinement regime at the Doppler laser cooling limit. Our measured cooling rate and final mode occupation are in good agreement with a semiclassical model which combines a Lindblad master equation solution for ion-photon interactions with classical harmonic oscillator motion of the trapped ion.

We analytically solve a model for light scattering in Ising dynamics of metastable atomic qubits, generalizing the approach of Foss-Feig {\it et al.}~[Phys.~Rev.~A {\bf 87}, 042101 (2013)] to include leakage outside the qubit manifold. We analyze the influence of these fundamental errors in simulations of proposed experiments with metastable levels of $^{40}$Ca$^+$ ions. We find that ``effective magnetic fields" generated by leaked qubits have significant impacts on spin-spin correlation functions for Greenberger-Horne-Zeilinger state preparation or for quantum simulations with strong coupling, while spin squeezing uses a much weaker coupling and is largely insensitive to the simulated leakage errors, even with a few hundred ions. Our theory and results are expected to be useful in modeling a variety of metastable qubit experiments in the future.

Pulsed laser ablation is an increasingly prevalent method for fast ion trap loading of various species, however characteristics of the ablation target source material can affect the ion-loading process. One factor which can reduce the atomic flux from a target is oxidation during atmospheric exposure when preparing or making changes to the ion trap vacuum system. Recent work has shown that perovskite ablation targets produce consistent atomic densities even after exposure to atmosphere when compared to elemental source targets. In this work, we directly compare calcium (Ca) and calcium-titanate (CaTiO$_3$) ablation targets, characterizing the neutral atomic beam flux using resonant, time-resolved absorption spectroscopy of the 423 nm $^{1}S_0 \rightarrow$ $^{1}P_1$ transition in neutral Ca. We measure the ablation plume longitudinal and transverse temperatures, number density, ion production, and spot lifetime for each target. In addition, we compare the ablated atomic beam density for both targets before and after 21 hours of exposure to atmosphere, demonstrating the relative robustness of the CaTiO$_3$ source.

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 $\sim 97\%$ 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 paper complete the set of operations for quantum simulation with the platform.

Ion transport is an essential operation in some models of quantum information processing, where fast ion shuttling with minimal motional excitation is necessary for efficient, high-fidelity quantum logic. While fast and cold ion shuttling has been demonstrated, the dynamics and specific trajectory of an ion during diabatic transport have not been studied in detail. Here we describe a position-dependent optical deshelving technique useful for sampling an ion's position throughout its trajectory, and we demonstrate the technique on fast linear transport of a $^{40}\text{Ca}^+$ ion in a surface-electrode ion trap. At high speed, the trap's electrode filters strongly distort the transport potential waveform. With this technique, we observe deviations from the intended constant-velocity (100 m/s) transport: we measure an average speed of 83(2) m/s and a peak speed of 251(6) m/s over a distance of 120 $μ$m

We report microwave spectroscopy of co-trapped $^9\text{Be}^+$ and $^{40}\text{Ca}^+$ within a compact permanent-magnet-based Penning ion trap. The trap is constructed with a reconfigurable array of NdFeB rings providing a 0.654 T magnetic field that is near the 0.6774-T magnetic-field-insensitive hyperfine transition in $^9\text{Be}^+$. Performing Ramsey spectroscopy on this hyperfine transition, we demonstrate nuclear spin coherence with a contrast decay time of >1 s. The $^9\text{Be}^+$ is sympathetically cooled by a Coulomb crystal of $^{40}\text{Ca}^+$, which minimizes $^9\text{Be}^+$ illumination and thus mitigates reactive loss. Introducing a unique high-magnetic-field optical detection scheme for $^{40}\text{Ca}^+$, we perform spin state readout without a 729~nm shelving laser. We record a fractional trap magnetic field instability below 20 ppb (<13 nT) at 43 s of averaging time with no magnetic shielding and only passive thermal isolation. We discuss potential applications of this compact, reconfigurable Penning trap.

We implement a two-qubit entangling Mølmer-Sørensen interaction by transporting two co-trapped $^{40}\mathrm{Ca}^{+}$ ions through a stationary, bichromatic optical beam within a surface-electrode Paul trap. We describe a procedure for achieving a constant Doppler shift during the transport which uses fine temporal adjustment of the moving confinement potential. The fixed interaction duration of the ions transported through the laser beam as well as the dynamically changing ac Stark shift require alterations to the calibration procedures used for a stationary gate. We use the interaction to produce Bell states with fidelities commensurate to those of stationary gates performed in the same system. This result establishes the feasibility of actively incorporating ion transport into quantum information entangling operations.

Entanglement generation in trapped-ion systems has relied thus far on two distinct but related geometric phase gate techniques: Molmer-Sorensen and light-shift gates. We recently proposed a variant of the light-shift scheme where the qubit levels are separated by an optical frequency [B. C. Sawyer and K. R. Brown, Phys. Rev. A 103, 022427 (2021)]. Here we report an experimental demonstration of this entangling gate using a pair of $^{40}$Ca$^+$ ions in a cryogenic surface-electrode ion trap and a commercial, high-power, 532 nm Nd:YAG laser. Generating a Bell state in 35 $μ$s, we directly measure an infidelity of $6(3) \times 10^{-4}$ without subtraction of experimental errors. The 532 nm gate laser wavelength suppresses intrinsic photon scattering error to $\sim 1 \times 10^{-5}$.

We propose an optical scheme for generating entanglement between co-trapped identical or dissimilar alkaline earth atomic ions ($^{40}\text{Ca}^+$, $^{88}\text{Sr}^+$, $^{138}\text{Ba}^+$, $^{226}\text{Ra}^+$) which exhibits fundamental error rates below $10^{-4}$ and can be implemented with a broad range of laser wavelengths spanning from ultraviolet to infrared. We also discuss straightforward extensions of this technique to include the two lightest Group-2 ions ($\text{Be}^+$, $\text{Mg}^+$) for multispecies entanglement. The key elements of this wavelength-insensitive geometric phase gate are the use of a ground ($S_{1/2}$) and a metastable ($D_{5/2}$) electronic state as the qubit levels within a $σ^z σ^z$ light-shift entangling gate. We present a detailed analysis of the principles and fundamental error sources for this gate scheme which includes photon scattering and spontaneous emission decoherence, calculating two-qubit-gate error rates and durations at fixed laser beam intensity over a large portion of the optical spectrum (300 nm to 2 $μ\text{m}$) for an assortment of ion pairs. We contrast the advantages and disadvantages of this technique against previous trapped-ion entangling gates and discuss its applications to quantum information processing and simulation with like and multispecies ion crystals.

To date, individual addressing of ion qubits has relied primarily on local Rabi or transition frequency differences between ions created via electromagnetic field spatial gradients or via ion transport operations. Alternatively, it is possible to synthesize arbitrary local one-qubit gates by leveraging local phase differences in a global driving field. Here we report individual addressing of $^{40}$Ca$^+$ ions in a two-ion crystal using axial potential modulation in a global gate laser field. We characterize the resulting gate performance via one-qubit randomized benchmarking, applying different random sequences to each co-trapped ion. We identify the primary error sources and compare the results with single-ion experiments to better understand our experimental limitations. These experiments form a foundation for the universal control of two ions, confined in the same potential well, with a single gate laser beam.

We report the design and experimental demonstration of a compact, reconfigurable Penning ion trap constructed with rare-earth permanent magnets placed outside of a trap vacuum enclosure. We describe the first observation of Doppler laser cooling of ions in a permanent magnet Penning trap. We detail a method for quantifying and optimizing the trap magnetic field uniformity in situ using a thermal beam of neutral $^{40}$Ca precursor atoms. Doppler laser cooling of $^{40}$Ca$^+$ is carried out at 0.65~T, and side-view images of trapped ion fluorescence show crystalline order for both two- and three-dimensional arrays. Measured $^{40}$Ca$^+$ trap frequencies confirm the magnetic field characterization with neutral $^{40}$Ca. The compact trap described here enables a variety of cold ion experiments with low size, weight, power, and cost requirements relative to traditional electromagnet-based Penning traps.

In trapped-ion quantum information processing, interactions between spins (qubits) are mediated by collective modes of motion of an ion crystal. While there are many different experimental strategies to design such interactions, they all face both technical and fundamental limitations to the achievable coherent interaction strength. In general, obtaining strong interactions and fast gates is an ongoing challenge. Here, we extend previous work [Phys. Rev. Lett. 112, 030501 (2019)] and present a general strategy for enhancing the interaction strengths in trapped-ion systems via parametric amplification of the ions' motion. Specifically, we propose a stroboscopic protocol using alternating applications of parametric amplification and spin-motion coupling. In comparison with the previous work, we show that the current protocol can lead to larger enhancements in the coherent interaction that increase exponentially with the gate time.

Quantum simulation of spin models can provide insight into complex problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. Here we study non-equilibrium, quantum spin dynamics arising from an engineered, homogeneous Ising interaction in a two-dimensional array of $^9$Be$^+$ ions in a Penning trap. We verify entanglement in the form of spin-squeezed states for up to 219 ions, directly observing 4.0$\pm$0.9 dB of spectroscopic enhancement. We also observe evidence of non-Gaussian, over-squeezed states in the full counting statistics. We find good agreement with ab-initio theory that includes competition between entanglement and decoherence, laying the groundwork for simulations of the transverse-field Ising model with variable-range interactions, for which numerical solutions are, in general, classically intractable.

We demonstrate photodissociation of BeH$^+$ ions within a Coulomb crystal of thousands of $^9$Be$^+$ ions confined in a Penning trap. Because BeH$^+$ ions are created via exothermic reactions between trapped, laser-cooled Be$^+$($^2\text{P}_{3/2}$) and background H$_2$ within the vacuum chamber, they represent a major contaminant species responsible for infidelities in large-scale trapped-ion quantum information experiments. The rotational-state-insensitive dissociation scheme described here makes use of 157 nm photons to produce Be$^+$ and H as products, thereby restoring Be$^+$ ions without the need for reloading. This technique facilitates longer experiment runtimes at a given background H$_2$ pressure, and may be adapted for removal of MgH$^+$ and AlH$^+$ impurities.

We employ spin-dependent optical dipole forces to characterize the transverse center-of-mass (COM) motional mode of a two-dimensional Wigner crystal of hundreds of $^9$Be$^+$. By comparing the measured spin dephasing produced by the spin-dependent force with the predictions of a semiclassical dephasing model, we obtain absolute mode temperatures in excellent agreement with both the Doppler laser cooling limit and measurements obtained from a previously published technique (B. C. Sawyer et al. Phys. Rev. Lett. \textbf{108}, 213003 (2012)). Furthermore, the structure of the dephasing histograms allows for discrimination between initial thermal and coherent states of motion. We also apply the techniques discussed here to measure, for the first time, the ambient heating rate of the COM mode of a 2D Coulomb crystal in a Penning trap. This measurement places an upper limit on the anomalous single-ion heating rate due to electric field noise from the trap electrode surfaces of $\frac{d\bar{n}}{dt}\sim 5$ s$^{-1}$ for our trap at a frequency of 795 kHz, where $\bar{n}$ is the mean occupation of quantized COM motion in the axial harmonic well.

By employing forces that depend on the internal electronic state (or spin) of an atomic ion, the Coulomb potential energy of a strongly coupled array of ions can be modified in a spin-dependent way to mimic effective quantum spin Hamiltonians. Both ferromagnetic and antiferromagnetic interactions can be implemented. We use simple models to explain how the effective spin interactions are engineered with trapped-ion crystals. We summarize the type of effective spin interactions that can be readily generated, and discuss an experimental implementation using single-plane ion crystals in a Penning trap.

We study the time evolution of correlation functions in long-range interacting quantum Ising models. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice dimension, both for ferromagnetic and antiferromagnetic coupling, and hence also in the presence of geometric frustration. In contrast to the nearest-neighbour case, we find that correlations decay like stretched or compressed exponentials in time. Provided the long-range character of the interactions is sufficiently strong, pronounced prethermalization plateaus are observed and relaxation timescales are widely separated. Specializing to a triangular lattice in two spatial dimensions, we propose to utilize these results for benchmarking of a recently developed ion-trap based quantum simulator.

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity. However, many properties of exotic strongly correlated spin systems (e.g., spin liquids) have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N~30 particles. Feynman divined that a quantum simulator - a special-purpose "analog" processor built using quantum particles (qubits) - would be inherently adept at such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach. However, simulations of quantum magnetism allowing controlled, tunable interactions between spins localized on 2D and 3D lattices of more than a few 10's of qubits have yet to be demonstrated, owing in part to the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction J_ij on a naturally occurring 2D triangular crystal lattice of hundreds of spin-1/2 particles (9Be+ ions stored in a Penning trap), a computationally relevant scale more than an order of magnitude larger than existing experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J_ij ~ 1/d_ij^a, where a is tunable over 0<a<3; d_ij is the distance between spin pairs. These power-laws correspond physically to infinite-range (a=0), Coulomb-like (a=1), monopole-dipole (a=2) and dipole-dipole (a=3) couplings. Experimentally, we demonstrate excellent agreement with theory for 0.05<a<1.4. This demonstration coupled with the high spin-count, excellent quantum control and low technical complexity of the Penning trap brings within reach simulation of interesting and otherwise computationally intractable problems in quantum magnetism.

We demonstrate spectroscopy and thermometry of individual motional modes in a mesoscopic 2D ion array using entanglement-induced decoherence as a method of transduction. Our system is a $\sim$400 $μ$m-diameter planar crystal of several hundred $^9$Be$^+$ ions exhibiting complex drumhead modes in the confining potential of a Penning trap. Exploiting precise control over the $^9$Be$^+$ valence electron spins, we apply a homogeneous spin-dependent optical dipole force to excite arbitrary transverse modes with an effective wavelength approaching the interparticle spacing ($\sim$20 \nolinebreak$μ$m). Center-of-mass displacements below 1 nm are detected via entanglement of spin and motional degrees of freedom.