Chapman Research Lab

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 present the design and characterization of a cryogenic vacuum chamber incorporating mechanical isolation from vibrations, a high numerical-aperture in-vacuum imaging objective, in-vacuum magnetic shielding, and an antenna for global radio-frequency manipulation of trapped ions. The cold shield near 4 K is mechanically referenced to an underlying optical table via thermally insulating supports and exhibits root-mean-square vibrations less than 7.61(4) nm. Using the in-vacuum objective, we can detect 397 nm photons from a trapped $^{40}\mathrm{Ca}^{+}$ ion with 1.77% efficiency and achieve 99.9963(4)% single-shot state-detection fidelity in 50 $μ$s. To characterize the efficacy of the magnetic shields, we perform Ramsey experiments on the ground state qubit and obtain a coherence time of 24(2) ms, which extends to 0.25(1) s with a single spin-echo pulse. XY4 and XY32 dynamical decoupling sequences driven via the radio-frequency antenna extend the coherence to 0.72(2) s and 0.81(3) s, respectively.

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.

The trapped-ion quantum charge-coupled device (QCCD) architecture is a leading candidate for advanced quantum information processing. In current QCCD implementations, imperfect ion transport and anomalous heating can excite ion motion during a calculation. To counteract this, intermediate cooling is necessary to maintain high-fidelity gate performance. Cooling the computational ions sympathetically with ions of another species, a commonly employed strategy, creates a significant runtime bottleneck. Here, we demonstrate a different approach we call exchange cooling. Unlike sympathetic cooling, exchange cooling does not require trapping two different atomic species. The protocol introduces a bank of "coolant" ions which are repeatedly laser cooled. A computational ion can then be cooled by transporting a coolant ion into its proximity. We test this concept experimentally with two $^{40}\mathrm{Ca}^{+}$ ions, executing the necessary transport in 107 $\mathrm{μs}$, an order of magnitude faster than typical sympathetic cooling durations. We remove over 96%, and as many as 102(5) quanta, of axial motional energy from the computational ion. We verify that re-cooling the coolant ion does not decohere the computational ion. This approach validates the feasibility of a single-species QCCD processor, capable of fast quantum simulation and computation.

Many-qubit Mølmer-Sørensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parameterizes these errors from simple experimental measurements, without free parameters. We validate the model in comparison with experiments that implement sequences of MS interactions on two $^{171}$Yb$^+$ ions. The model shows reasonable agreement after several MS interactions as quantified by the reduced chi-squared statistic $χ^2_\mathrm{red} \approx 2$. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are $91\%$ and $83\%$ of the optimal theoretical values. Our model predicts $0.93^{+0.03}_{-0.02}$ and $0.95^{+0.04}_{-0.03}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations the model achieves approximation ratios that are 99$\%$ of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.

Ion trap quantum hardware promises to provide a computational advantage over classical computing for specific problem spaces while also providing an alternative hardware implementation path to cryogenic quantum systems as typified by IBM's quantum hardware. However, programming ion trap systems currently requires both strategies to mitigate high levels of noise and also tools to ease the challenge of programming these systems with pulse- or gate-level operations. This work focuses on improving the state-of-the-art for quantum programming of ion trap testbeds through the use of a quantum language specification, QCOR, and by demonstrating multi-level optimizations at the language, intermediate representation, and hardware backend levels. We implement a new QCOR/XACC backend to target a general ion trap testbed and then demonstrate the usage of multi-level optimizations to improve circuit fidelity and to reduce gate count. These techniques include the usage of a backend-specific numerical optimizer and physical gate optimizations to minimize the number of native instructions sent to the hardware. We evaluate our compiler backend using several QCOR benchmark programs, finding that on present testbed hardware, our compiler backend maintains the number of two-qubit native operations but decreases the number of single-qubit native operations by 1.54 times compared to the previous compiler regime. For projected testbed hardware upgrades, our compiler sees a reduction in two-qubit native operations by 2.40 times and one-qubit native operations by 6.13 times.

In order to quantify the relative performance of different testbed quantum computing devices, it is useful to benchmark them using a common protocol. While some benchmarks rely on the performance of random circuits and are generic in nature, here we instead propose and implement a practical, application-based benchmark. In particular, our protocol calculates the energy of the ground state in the single particle subspace of a 1-D Fermi Hubbard model, a problem which is efficient to solve classically. We provide a quantum ansatz for the problem that is provably able to probe the full single particle subspace for a general length 1-D chain and scales efficiently in number of gates and measurements. Finally, we demonstrate and analyze the benchmark performance on superconducting and ion trap testbed hardware from three hardware vendors and with up to 24 qubits.

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 present a framework for quantum process tomography of two-ion interactions that leverages modulations of the trapping potential and composite pulses from a global laser beam to achieve individual-ion addressing. Tomographic analysis of identity and delay processes reveals dominant error contributions from laser decoherence and slow qubit frequency drift during the tomography experiment. We use this framework on two co-trapped $^{40}$Ca$^+$ ions to analyze both an optimized and an overpowered Mølmer-Sørensen gate and to compare the results of this analysis to a less informative Bell-state tomography measurement and to predictions based on a simplified noise model. These results show that the technique is effective for the characterization of two-ion quantum processes and for the extraction of meaningful information about the errors present in the system. The experimental convenience of this method will allow for more widespread use of process tomography for characterizing entangling gates in trapped-ion systems.

We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion quantum hardware to find approximate solutions to Max-Cut. We present a mathematical description of the problem and provide approximately optimal algorithmic constructions that generate arbitrary unweighted coupling graphs with $n$ nodes in $O(n)$ global entangling operations and weighted graphs with $m$ edges in $O(m)$ operations. These upper bounds are not tight in general, and we formulate a mixed-integer program to solve the graph coupling problem to optimality. We perform numeric experiments on small graphs with $n\le8$ and show that optimal sequences, which use fewer operations, can be found using mixed-integer programs. Noisy simulations of Max-Cut QAOA show that our implementation is less susceptible to noise than the standard gate-based compilation.

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.

Trapped ions offer a pristine platform for quantum computation and simulation, but improving their coherence remains a crucial challenge. Here, we propose and analyze a new strategy to enhance the coherent interactions in trapped ion systems via parametric amplification of the ions' motion--by squeezing the collective motional modes (phonons), the spin-spin interactions they mediate can be significantly enhanced. We illustrate the power of this approach by showing how it can enhance collective spin states useful for quantum metrology, and how it can improve the speed and fidelity of two-qubit gates in multi-ion systems, important ingredients for scalable trapped ion quantum computation. Our results are also directly relevant to numerous other physical platforms in which spin interactions are mediated by bosons.

We present a technique to measure the amplitude of a center-of-mass (COM) motion of a two-dimensional ion crystal of $\sim$100 ions. By sensing motion at frequencies far from the COM resonance frequency, we experimentally determine the technique's measurement imprecision. We resolve amplitudes as small as 50 pm, 40 times smaller than the COM mode zero-point fluctuations. The technique employs a spin-dependent, optical-dipole force to couple the mechanical oscillation to the electron spins of the trapped ions, enabling a measurement of one quadrature of the COM motion through a readout of the spin state. We demonstrate sensitivity limits set by spin projection noise and spin decoherence due to off-resonant light scattering. When performed on resonance with the COM mode frequency, the technique demonstrated here can enable the detection of extremely weak forces ($< \,$1 yN) and electric fields ($< \,$1 nV/m), providing an opportunity to probe quantum sensing limits and search for physics beyond the standard model.

Quantum networking links quantum processors through remote entanglement for distributed quantum information processing (QIP) and secure long-range communication. Trapped ions are a leading QIP platform, having demonstrated universal small-scale processors and roadmaps for large-scale implementation. Overall rates of ion-photon entanglement generation, essential for remote trapped ion entanglement, are limited by coupling efficiency into single mode fibres5 and scaling to many ions. Here we show a microfabricated trap with integrated diffractive mirrors that couples 4.1(6)% of the fluorescence from a $^{174}$Yb$^+$ ion into a single mode fibre, nearly triple the demonstrated bulk optics efficiency. The integrated optic collects 5.8(8)% of the π transition fluorescence, images the ion with sub-wavelength resolution, and couples 71(5)% of the collected light into the fibre. Our technology is suitable for entangling multiple ions in parallel and overcomes mode quality limitations of existing integrated optical interconnects. In addition, the efficiencies are sufficient for fault tolerant QIP.

We control the relative coupling strength of carrier and first order motional sideband interactions of a trapped ion by placing it in a resonant optical standing wave. Our configuration uses the surface of a microfabricated chip trap as a mirror, avoiding technical challenges of in-vacuum optical cavities. Displacing the ion along the standing wave, we show a periodic suppression of the carrier and sideband transitions with the cycles for the two cases $180^\circ$ out of phase with each other. This technique allows for suppression of off-resonant carrier excitations when addressing the motional sidebands, with applications in quantum simulation and quantum control. Using the standing wave fringes, we measure the relative ion height as a function of applied electric field, allowing for a precise measurement of ion displacement and, combined with measured micromotion amplitudes, a validation of trap numerical models.

State-of-the-art microfabricated ion traps for quantum information research are approaching nearly one hundred control electrodes. We report here on the development and testing of a new architecture for microfabricated ion traps, built around ball-grid array (BGA) connections, that is suitable for increasingly complex trap designs. In the BGA trap, through-substrate vias bring electrical signals from the back side of the trap die to the surface trap structure on the top side. Gold-ball bump bonds connect the back side of the trap die to an interposer for signal routing from the carrier. Trench capacitors fabricated into the trap die replace area-intensive surface or edge capacitors. Wirebonds in the BGA architecture are moved to the interposer. These last two features allow the trap die to be reduced to only the area required to produce trapping fields. The smaller trap dimensions allow tight focusing of an addressing laser beam for fast single-qubit rotations. Performance of the BGA trap as characterized with $^{40}$Ca$^+$ ions is comparable to previous surface-electrode traps in terms of ion heating rate, mode frequency stability, and storage lifetime. We demonstrate two-qubit entanglement operations with $^{171}$Yb$^+$ ions in a second BGA trap.

Quantum simulation - the use of one quantum system to simulate a less controllable one - may provide an understanding of the many quantum systems which cannot be modeled using classical computers. Impressive progress on control and manipulation has been achieved for various quantum systems, but one of the remaining challenges is the implementation of scalable devices. In this regard, individual ions trapped in separate tunable potential wells are promising. Here we implement the basic features of this approach and demonstrate deterministic tuning of the Coulomb interaction between two ions, independently controlling their local wells. The scheme is suitable for emulating a range of spin-spin interactions, but to characterize the performance of our setup we select one that entangles the internal states of the two ions with 0.82(1) fidelity. Extension of this building-block to a 2D-network, which ion-trap micro-fabrication processes enable, may provide a new quantum simulator architecture with broad flexibility in designing and scaling the arrangement of ions and their mutual interactions. To perform useful quantum simulations, including those of intriguing condensed-matter phenomena such as the fractional quantum Hall effect, an array of tens of ions might be sufficient.

We measure ion heating following transport throughout a Y-junction surface-electrode ion trap. By carefully selecting the trap voltage update rate during adiabatic transport along a trap arm, we observe minimal heating relative to the anomalous heating background. Transport through the junction results in an induced heating between 37 and 150 quanta in the axial direction per traverse. To reliably measure heating in this range, we compare the experimental sideband envelope, including up to fourth-order sidebands, to a theoretical model. The sideband envelope method allows us to cover the intermediate heating range inaccessible to the first-order sideband and Doppler recooling methods. We conclude that quantum information processing in this ion trap will likely require sympathetic cooling in order to support high fidelity gates after junction transport.

The advent of microfabricated ion traps for the quantum information community has allowed research groups to build traps that incorporate an unprecedented number of trapping zones. However, as device complexity has grown, the number of digital-to-analog converter (DAC) channels needed to control these devices has grown as well, with some of the largest trap assemblies now requiring nearly one hundred DAC channels. Providing electrical connections for these channels into a vacuum chamber can be bulky and difficult to scale beyond the current numbers of trap electrodes. This paper reports on the development and testing of an in-vacuum DAC system that uses only 9 vacuum feedthrough connections to control a 78-electrode microfabricated ion trap. The system is characterized by trapping single and multiple $^{40}$Ca$^+$ ions. The measured axial mode stability, ion heating rates, and transport fidelities for a trapped ion are comparable to systems with external(air-side) commercial DACs.

Selective laser addressing of a single atom or atomic ion qubit can be improved using narrowband composite pulse sequences. We describe a Lie-algebraic technique to generalize known narrowband sequences and introduce new sequences related by dilation and rotation of sequence generators. Our method improves known narrowband sequences by decreasing both the pulse time and the residual error. Finally, we experimentally demonstrate these composite sequences using $^{40}$Ca$^+$ ions trapped in a surface-electrode ion trap.

We schedule the Steane [[7,1,3]] error correction on a model ion trap architecture with ballistic transport. We compare the level one error rates for syndrome extraction using the Shor method of ancilla prepared in verified cat states to the DiVincenzo-Aliferis method without verification. The study examines how the quantum error correction circuit latency and error vary with the number of available ancilla and the choice of protocol for ancilla preparation and measurement. We find that with few exceptions the DiVincenzo-Aliferis method without cat state verification outperforms the standard Shor method. We also find that additional ancilla always reduces the latency but does not significantly change the error due to the high memory fidelity.

We present a microfabricated surface-electrode ion trap with a pair of integrated waveguides that generate a standing microwave field resonant with the 171Yb+ hyperfine qubit. The waveguides are engineered to position the wave antinode near the center of the trap, resulting in maximum field amplitude and uniformity along the trap axis. By calibrating the relative amplitudes and phases of the waveguide currents, we can control the polarization of the microwave field to reduce off-resonant coupling to undesired Zeeman sublevels. We demonstrate single-qubit pi-rotations as fast as 1 us with less than 6 % variation in Rabi frequency over an 800 um microwave interaction region. Fully compensating pulse sequences further improve the uniformity of X-gates across this interaction region.

We present a simple cryostat purpose built for use with surface-electrode ion traps, designed around an affordable, large cooling power commercial pulse tube refrigerator. A modular vacuum enclosure with a single vacuum space facilitates interior access, and enables rapid turnaround and flexiblity for future modifications. Long rectangular windows provide nearly 360 degrees of optical access in the plane of the ion trap, while a circular bottom window near the trap enables NA 0.4 light collection without the need for in-vacuum optics. We evaluate the system's mechanical and thermal characteristics, and we quantify ion trapping performance by trapping 40Ca+, finding small stray electric fields, long ion lifetimes, and low ion heating rates.

Atomic ions confined in multi-electrode traps have been proposed as a basis for scalable quantum information processing. This scheme involves transporting ions between spatially distinct locations by use of time-varying electric potentials combined with laser or microwave pulses for quantum logic in specific locations. We report the development of a fast multi-channel arbitrary waveform generator for applying the time-varying electric potentials used for transport and for shaping quantum logic pulses. The generator is based on a field-programmable gate array controlled ensemble of 16-bit digital-to-analog converters with an update frequency of 50 MHz and an output range of $\pm$10 V. The update rate of the waveform generator is much faster than relevant motional frequencies of the confined ions in our experiments, allowing diabatic control of the ion motion. Numerous pre-loaded sets of time-varying voltages can be selected with 40 ns latency conditioned on real-time signals. Here we describe the device and demonstrate some of its uses in ion-based quantum information experiments, including speed-up of ion transport and the shaping of laser and microwave pulses.

We report the design, fabrication, and characterization of a microfabricated surface-electrode ion trap that supports controlled transport through the two-dimensional intersection of linear trapping zones arranged in a ninety-degree cross. The trap is fabricated with very-large-scalable-integration (VLSI) techniques which are compatible with scaling to a larger quantum information processor. The shape of the radio-frequency (RF) electrodes is optimized with a genetic algorithm to minimize axial pseudopotential barriers and to minimize ion heating during transport. Seventy-eight independent DC control electrodes enable fine control of the trapping potentials. We demonstrate reliable ion transport between junction legs, trapping of ion chains with nearly-equal spacing in one of the trap's linear sections, and merging and splitting ions from these chains. Doppler-cooled ions survive more than 10^5 round-trip transits between junction legs without loss and more than sixty-five consecutive round trips without laser cooling.

Recent advances in quantum information processing with trapped ions have demonstrated the need for new ion trap architectures capable of holding and manipulating chains of many (>10) ions. Here we present the design and detailed characterization of a new linear trap, microfabricated with scalable complementary metal-oxide-semiconductor (CMOS) techniques, that is well-suited to this challenge. Forty-four individually controlled DC electrodes provide the many degrees of freedom required to construct anharmonic potential wells, shuttle ions, merge and split ion chains, precisely tune secular mode frequencies, and adjust the orientation of trap axes. Microfabricated capacitors on DC electrodes suppress radio-frequency pickup and excess micromotion, while a top-level ground layer simplifies modeling of electric fields and protects trap structures underneath. A localized aperture in the substrate provides access to the trapping region from an oven below, permitting deterministic loading of particular isotopic/elemental sequences via species-selective photoionization. The shapes of the aperture and radio-frequency electrodes are optimized to minimize perturbation of the trapping pseudopotential. Laboratory experiments verify simulated potentials and characterize trapping lifetimes, stray electric fields, and ion heating rates, while measurement and cancellation of spatially-varying stray electric fields permits the formation of nearly-equally spaced ion chains.

Motivated by recent developments in ion trap design and fabrication, we investigate the stability of ion motion in asymmetrical, planar versions of the classic Paul trap. The equations of motion of an ion in such a trap are generally coupled due to a nonzero relative angle $θ$ between the principal axes of RF and DC fields, invalidating the assumptions behind the standard stability analysis for symmetric Paul traps. We obtain stability diagrams for the coupled system for various values of $θ$, generalizing the standard $q$-$a$ stability diagrams. We use multi-scale perturbation theory to obtain approximate formulas for the boundaries of the primary stability region and obtain some of the stability boundaries independently by using the method of infinite determinants. We cross-check the consistency of the results of these methods. Our results show that while the primary stability region is quite robust to changes in $θ$, a secondary stability region is highly variable, joining the primary stability region at the special case of $θ=45^{\circ}$, which results in a significantly enlarged stability region for this particular angle. We conclude that while the stability diagrams for classical, symmetric Paul traps are not entirely accurate for asymmetric surface traps (or for other types of traps with a relative angle between the RF and DC axes), they are safe in the sense that operating conditions deemed stable according to standard stability plots are in fact stable for asymmetric traps, as well. By ignoring the coupling in the equations, one only underestimates the size of the primary stability region.

In ion trap quantum information processing, efficient fluorescence collection is critical for fast, high-fidelity qubit detection and ion-photon entanglement. The expected size of future many-ion processors require scalable light collection systems. We report on the development and testing of a microfabricated surface-electrode ion trap with an integrated high numerical aperture (NA) micromirror for fluorescence collection. When coupled to a low NA lens, the optical system is inherently scalable to large arrays of mirrors in a single device. We demonstrate stable trapping and transport of 40Ca+ ions over a 0.63 NA micromirror and observe a factor of 1.9 enhancement in photon collection compared to the planar region of the trap.

We describe a novel monolithic ion trap that combines the flexibility and scalability of silicon microfabrication technologies with the superior trapping characteristics of traditional four-rod Paul traps. The performace of the proposed microfabricated trap approaches that of the macroscopic structures. The fabrication process creates an angled through-chip slot which allows backside ion loading and through-laser access while avoiding surface light scattering and dielectric charging. The trap geometry and dimensions are optimized for confining long ion chains with equal ion spacing [G.-D. Lin, et al., Europhys. Lett. 86, 60004 (2009)]. Control potentials have been derived to produce linear, equally spaced ion chains of up to 50 ions spaced at 10 um. With the deep trapping depths achievable in this design, we expect that these chains will be sufficiently long-lived to be used in quantum simulations of magnetic systems [E.E. Edwards, et al., Phys. Rev. B 82, 060412(R) (2010)]. The trap is currently being fabricated at Georgia Tech using VLSI techniques.

A scalable, multiplexed ion trap for quantum information processing is fabricated and tested. The trap design and fabrication process are optimized for scalability to small trap size and large numbers of interconnected traps, and for integration of control electronics and optics. Multiple traps with similar designs are tested with Cd+, Mg+, and Sr+ ions at room temperature and with Sr+ at 6 K, with respective ion lifetimes of 90 s, 300 +/- 30 s, 56 +/- 6 s, and 4.5 +/- 1.1 hours. The motional heating rate for Mg+ at room temperature and a trap frequency of 1.6 MHz is measured to be 7 +/- 3 quanta per millisecond. For Sr+ at 6 K and 540 kHz the heating rate is measured to be 220 +/- 30 quanta per second.