Eric R. Hudson

Trapped ions provide a high-fidelity platform for quantum information processing, yet delivery of multiple, distinct wavelengths across large networks of interaction zones remains a bottleneck. Conventional free-space light delivery lacks scalability, while on-chip grating couplers suffer from narrow operational bandwidth that increases circuit footprint and optical interfacing complexity. Here we show a broadband photonic integrated circuit capable of addressing individual ions. The circuit combines a planar waveguide lens with a micromirror fabricated using two-photon polymerization at wafer scale. This implementation can address three individual ions from $λ$ = 405 - 880 nm with -27 dB average intensity crosstalk at $5\,μ\mathrm{m}$ pitch. We trap $^{40}\mathrm{Ca}^{+}$ and $^{138}\mathrm{Ba}^{+}$ ions above such devices, characterize optical crosstalk with barium ions, and demonstrate individual repumping of calcium ions. This monolithic photonic architecture brings broadband addressing in an on-chip modality to trapped-ion technology. More generally, integrating additive manufacturing into quantum devices is poised to unlock expanded design space for implementing novel quantum architectures.

The Th-229 nuclear isomeric state has the lowest energy of all known nuclear excited states, placing it within the reach of current table-top laser technology. This extraordinary property has made this nuclear isomer an attractive candidate for a nuclear optical clock of incredibly high precision and accuracy, both as isolated trapped Th-229 ions and embedded into solid-state platforms. Activity around Th-229 has surged in recent years, driven by breakthroughs in its direct laser excitation. The underlying nuclear physics that gives rise to this unique isomer will be elucidated, as well as the nearly half-century of efforts that led to its direct excitation. The design and systematics of a Th-229 nuclear clock will be discussed, both in ion traps and in the solid-state. These systematics, such as frequency shifts and quenching channels, can be leveraged both to probe the local chemical environment, and as a control knob during clock operation. Finally, the nuclear clock's high sensitivity to the variations of fundamental constants will be discussed.

Engineering large-scale quantum computers which simultaneously provide high-fidelity quantum operations, low memory errors, low crosstalk, and reasonable resource usage remains an outstanding challenge across quantum computing platforms. In trapped ions, progress has largely focused on alkaline-earth and ytterbium ions, whose simple electronic structures facilitate control over their internal state. Here we investigate singly-ionized yttrium ($^{89}\mathrm{Y}^+$), a two-valence-electron ion whose ground-state manifold hosts a nuclear-spin qubit and which also features a variety of low-lying metastable manifolds, for applications in quantum information processing. Because experimental data are limited, we perform high-resolution laser-induced fluorescence spectroscopy to measure the hyperfine structure of several low-lying levels, and carry out comprehensive electronic structure calculations to determine lifetimes, transition matrix elements, and hyperfine coefficients for manifolds addressable with visible, near-visible, or infrared wavelengths. Using these results, we analyze schemes for qubit storage, initialization, readout, leakage mitigation, and single- and two-qubit gates. These results position $^{89}\mathrm{Y}^+$ as a uniquely capable next-generation trapped-ion qubit, combining field-insensitive nuclear-spin or clock-qubit storage with spectrally isolated transitions for operations.

We report a theoretical and experimental investigation of autoionizing resonances from the $5d6p\,{}^3\mathrm{D}_1^o$ manifold in neutral barium for efficient loading of ion traps. Our calculations predict large resonant cross sections for many narrow autoionizing resonances, but we find experimentally that for most of these, Doppler broadening during trap loading depresses the effective cross sections that can be achieved in practice. We identify and demonstrate a strong, broad transition at $531\,\mathrm{nm}$, and show that it furnishes an order-of-magnitude increase in trap loading efficiency compared to other demonstrated resonances.

While laser excitation of the nuclear isomeric transition in $^{229}$Th has been recently achieved for thorium atoms embedded in large-bandgap crystals, laser excitation and characterization of the nuclear transition in trapped $^{229}$Th$^{3+}$ ions has not yet been accomplished. To address these experiments, a cryogenic Paul trap setup has been designed, built, and commissioned at LMU Munich. Here, we present the specifications of the new experimental platform and demonstrate its successful operation, showing the extraction, subsequent ion-guiding, mass-purification, and trapping of $^{229}$Th$^{3+}$ and $^{229\text{m}}$Th$^{3+}$ ions from a newly designed buffer-gas stopping cell as well as of $^{88}$Sr$^{+}$ ions from laser ablation of a solid target. Further, we show sympathetic laser cooling of $^{229\text{(m)}}$Th$^{3+}$ by Doppler-cooled $^{88}$Sr$^{+}$ ions and the formation of mixed-species Coulomb crystals.

Recent advances in laser excitation of the low-energy nuclear isomer transition in $^{229}$Th have opened avenues for developing nuclear clocks, a novel quantum technology with exceptional performance and sensitivity to exotic physics. Here we explore the host-dependence of the nuclear clock frequency, focusing on the isomer shift induced by the difference in the nuclear charge distribution between the ground and excited nuclear states. We combine relativistic many-body methods of atomic structure with periodic density functional theory to evaluate the isomer shifts in solid-state hosts. We elucidate the critical importance of the ``relaxation'' effect in evaluating the isomer shifts. Our analysis predicts nuclear clock frequencies for various solid-state and trapped ion platforms: $ ω_\text{clk}(\text{solid state}) = 2,020,407,384(40) \, \text{MHz}$, $ω_\text{clk}(^{229}\text{Th}^{4+}) = 2,020,407,648(70) \, \text{MHz}$, and $ ω_\text{clk}(^{229}\text{Th}^{3+}) = 2,020,407,114(70) \, \text{MHz}$. We also determine the nuclear transition energy for the bare $^{229}$Th nucleus to be $ω_\text{nuc} = 8.272(22) \,\text{eV}$. Our calculated valence-band isomer shifts for different host materials constrain the nuclear transition frequencies to an 80 MHz-wide frequency window, aiding experimental searches for the $^{229}$Th nuclear transition in novel materials.

Ultrasensitive detection of the frequency, phase, and amplitude of radio frequency (RF) electric fields is central to a variety of important applications, including radio communication, cosmology, dark matter searches, and high-fidelity qubit control. Quantum harmonic oscillator (QHO) systems, especially trapped ions, have been used with several quantum sensing techniques to achieve electric field sensing with state-of-the-art sensitivity and nanometer spatial resolution. However, these systems are limited to a narrow frequency range centered around either the motional frequency of the trapped ion oscillator or the frequency of an optical transition in the ion; often these techniques are not sensitive to the RF phase. Here, we propose and demonstrate a procedure that unlocks the extreme sensitivity of a QHO to allow high precision wideband detection of the frequency, phase, and amplitude of an unknown electric field. Specifically, we use motional Raman transitions in a single trapped ion, cooled near its motional ground state to realize state of the art sensitivities to frequency, phase, and amplitude, and show the technique works over a frequency range that is >800x larger than previous techniques. Further, this technique is shown to be compatible with both quantum amplification via squeezing and measurement in the Fock basis, allowing performance 3.4(20) dB below the standard quantum limit and the potential for several orders of magnitude improvement in sensitivity with moderate upgrades. In addition to providing an attractive platform for quantum sensing of small fields, this technique allows in situ calibration of qubit control lines in QHO systems, as well as transduction of external, non-resonant drives into oscillator excitation. Additionally, this approach can be extended to other QHO systems, such as a superconducting qubit-resonator system.

The lifetime of Ba$^+$ ions confined in a Paul trap is found, under typical conditions, to be limited by chemical reactions with residual background gas. An integrated ion trap and time-of-flight mass spectrometer are used to analyze the reactions of the trapped Ba$^+$ ions with three common gases in an ultrahigh vacuum system (H$_2$, CO$_2$ and H$_2$O). It is found that the products of these reactions can all be photodissociated by a single ultraviolet laser at 225~nm, thereby allowing the recovery of the Ba$^+$ ions and leading to an increase of the effective trap lifetime. For a Coulomb crystal, the lifetime increased from roughly 6~hours to 2~days at room temperature. It is suggested that higher enhancement factors are possible in systems with stronger traps. In addition, photodissociation wavelengths for other common trapped ion systems are provided.

Trapped Be+ ions are a leading platform for quantum information science [1], but reactions with background gas species, such as H2 and H2O, result in qubit loss. Our experiment reveals that the BeOH+ ion is the final trapped ion species when both H2 and H2O exist in a vacuum system with cold, trapped Be+. To understand the loss mechanism, low-temperature reactions between sympathetically cooled BeD+ ions and H2O molecules have been investigated using an integrated, laser-cooled Be+ ion trap and high-resolution Time-of-Flight (TOF) mass spectrometer (MS) [2]. Among all the possible products,BeH2O+, H2DO+, BeOD+, and BeOH+, only the BeOH+ molecular ion was observed experimentally, with the assumed co-product of HD. Theoretical analyses based on explicitly correlated restricted coupled cluster singles, doubles, and perturbative triples (RCCSD(T)-F12) method with the augmented correlation-consistent polarized triple zeta (AVTZ) basis set reveal that two intuitive direct abstraction product channels, Be + H2DO+ and D + BeH2O+, are not energetically accessible at the present reaction temperature (~150 K). Instead, a double displacement BeOH+ + HD product channel is accessible due to a large exothermicity of 1.885 eV through a submerged barrier in the reaction pathway. While the BeOD+ + H2 product channel has a similar exothermicity, the reaction pathway is dynamically unfavourable, as suggested by a Sudden Vector Projection analysis. This work sheds light on the origin of the loss and contaminations of the laser-cooled Be+ ions in quantum-information experiments.

Internal states of polar molecules can be controlled by microwave-frequency electric dipole transitions. If the applied microwave electric field has a spatial gradient, these transitions also affect the motion of these dipolar particles. This capability can be used to engineer phonon-mediated quantum gates between e.g. trapped polar molecular ion qubits without laser illumination and without the need for cooling near the motional ground state. The result is a high-speed quantum processing toolbox for dipoles in thermal motion that combines the precision microwave control of solid-state qubits with the long coherence times of trapped ion qubits.

Dipole-phonon quantum logic (DPQL) leverages the interaction between polar molecular ions and the motional modes of a trapped-ion Coulomb crystal to provide a potentially scalable route to quantum information science. Here, we study a class of candidate molecular ions for DPQL, the cationic alkaline-earth monoxides and monosulfides, which possess suitable structure for DPQL and can be produced in existing atomic ion experiments with little additional complexity. We present calculations of DPQL operations for one of these molecules, CaO$^+$, and discuss progress towards experimental realization. We also further develop the theory of DPQL to include state preparation and measurement and entanglement of multiple molecular ions.

The interaction between the electric dipole moment of a trapped molecular ion and the configuration of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a co-trapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that virtual phonon exchange can significantly boost range of the intermolecular dipole-dipole interaction, allowing strong coupling between widely-separated molecular ion qubits.

We study an excited atom-polar molecular ion chemical reaction (Ca$^*$ + BaCl$^+$) at low temperature by utilizing a hybrid atom-ion trapping system. The reaction rate and product branching fractions are measured and compared to model calculations as a function of both atomic quantum state and collision energy. At the lowest collision energy we find that the chemical dynamics dramatically differ from capture theory predictions and are primarily dictated by the radiative lifetime of the atomic quantum state instead of the underlying excited-state interaction potential. We provide a simple rule for calculating at what temperature this regime, where the collision complex lifetime is longer than the radiative lifetime of the quantum state, is reached. This effect, which greatly suppresses the reactivity of short-lived excited states, provides a means for directly probing reaction range. It also naturally suppresses unwanted chemical reactions in hybrid trapping experiments, allowing longer molecular ion coherence and interrogation times.

$^{229}$Th is the only nucleus currently under investigation for the development of a nuclear optical clock (NOC) of ultra-high accuracy. The insufficient knowledge of the first nuclear excitation energy of $^{229}$Th has so far hindered direct nuclear laser spectroscopy of thorium ions and thus the development of a NOC. Here, a nuclear laser excitation scheme is detailed, which makes use of thorium atoms instead of ions. This concept, besides potentially leading to the first nuclear laser spectroscopy, would determine the isomeric energy to 40 $μ$eV resolution, corresponding to 10 GHz, which is a $10^4$ times improvement compared to the current best energy constraint. This would determine the nuclear isomeric energy to a sufficient accuracy to allow for nuclear laser spectroscopy of individual thorium ions in a Paul trap and thus the development of a single-ion nuclear optical clock.

An important physical process unique to neutral-ion systems is the charge-transfer (CT) reaction. Here, we present measurements of and models for CT processes between co-trapped ultracold Ca atoms and Yb ions under well-controlled conditions. The theoretical analysis reveals the existence of three reaction mechanisms when lasers from a magneto-optical trap (MOT) and an additional catalyst laser are present. Besides the direct CT involving existent excited Ca population in the MOT, the second pathway is controlled by MOT-induced CT, whereas the third one mostly involves the additional red-detuned laser.

We demonstrate an ion shuttling technique for high-resolution control of atom-ion collision energy by translating an ion held within a radio-frequency trap through a magneto-optical atom trap. The technique is demonstrated both experimentally and through numerical simulations, with the experimental results indicating control of ion kinetic energies from $0.05-1$ K with a fractional resolution of $\sim10$ and the simulations demonstrating that kinetic energy control up to $120$ K with a maximum predicted resolution of $\sim100$ is possible, offering order-of-magnitude improvements over most alternative techniques. Lastly, we perform a proof-of-principle chemistry experiment using this technique and outline how the method may be refined in the future and applied to the study of molecular ion chemistry.

We consider the practical feasibility of using the direct, electric dipole-dipole interaction between co-trapped molecular ions for robust quantum logic without the need for static polarizing fields. The use of oscillating dipole moments, as opposed to static electric dipoles, dynamically decouples the dipoles from laboratory fields, including the electric fields of the trap itself. Further, this implementation does not require quantum control of motion, potentially removing a major roadblock to ion trap quantum computing scalability. Since the polarizing field is electromagnetic radiation, even pairs of states with splittings in the THz regime can be fully polarized.

Hypermetallic alkaline earth (M) oxides of formula MOM have been studied under plasma conditions that preclude insight into their formation mechanism. We present here the application of emerging techniques in ultracold physics to the synthesis of a mixed hypermetallic oxide, BaOCa$^+$. These methods, augmented by high-level electronic structure calculations, permit detailed investigation of the bonding and structure, as well as the mechanism of its formation via the barrierless reaction of Ca $(^3P_J)$ with BaOCH$_{3}^+$. Further investigations of the reaction kinetics as a function of collision energy over the range 0.005 K to 30 K and of individual Ca fine-structure levels compare favorably with calculations based on long-range capture theory.

$^{133}\text{Ba}^+$ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus and visible wavelength electronic transitions. Using a microgram source of radioactive material, we trap and laser-cool the synthetic $A$ = 133 radioisotope of barium II in a radio-frequency ion trap. Using the same, single trapped atom, we measure the isotope shifts and hyperfine structure of the $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $6^2 \text{S}_{1/2}$ and $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $5^2 \text{D}_{3/2}$ electronic transitions that are needed for laser cooling, state preparation, and state detection of the clock-state hyperfine and optical qubits. We also report the $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $5^2 \text{D}_{3/2}$ electronic transition isotope shift for the rare $A$ = 130 and 132 barium nuclides, completing the spectroscopic characterization necessary for laser cooling all long-lived barium II isotopes.

Sympathetic cooling of trapped ions through collisions with neutral buffer gases is critical to a variety of modern scientific fields, including fundamental chemistry, mass spectrometry, nuclear and particle physics, and atomic and molecular physics. Despite its widespread use over four decades, there remain open questions regarding its fundamental limitations. To probe these limits, here we examine the steady-state evolution of up to ten barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behavior as evidenced by bifurcations in the ion steady-state temperature, parameterized by ion number. We show that this behavior leads to limitations in creating and maintaining translationally cold samples of trapped ions using neutral-gas sympathetic cooling. These results may provide a route to studying nonequilibrium thermodynamics.

We have performed a combined experimental and theoretical study of the photodissociation cross section of the molecular ion DyCl$^+$. The photodissociation cross section for the photon energy range 35,500 cm$^{-1}$ to 47,500 cm$^{-1}$ is measured using an integrated ion trap and time-of-flight mass spectrometer; we observe a broad, asymmetric profile that is peaked near 43,000 cm$^{-1}$. The theoretical cross section is determined from electronic potentials and transition dipole moments calculated using the relativistic configuration-interaction valence-bond and coupled-cluster methods. The electronic structure of DyCl$^+$ is extremely complex due to the presence of multiple open electronic shells, including the 4f$^{10}$ configuration. The molecule has nine attractive potentials with ionically-bonded electrons and 99 repulsive potentials dissociating to a ground state Dy$^+$ ion and Cl atom. We explain the lack of symmetry in the cross section as due to multiple contributions from one-electron-dominated transitions between the vibrational ground state and several resolved repulsive excited states.

Recently, we reported an ion trap experiment with an integrated time-of-flight mass spectrometer (TOFMS) [Phys. Rev. Appl. 2, 034013 (2014)] focussing on the improvement of mass resolution and detection limit due to sample preparation at millikelvin temperatures. The system utilizes a radio-frequency (RF) ion trap with asymmetric drive for storing and manipulating laser-cooled ions and features radial extraction into a compact $275$ mm long TOF drift tube. The mass resolution exceeds $m / Δm = 500$, which provides isotopic resolution over the whole mass range of interest in current experiments and constitutes an improvement of almost an order of magnitude over other implementations. In this manuscript, we discuss the experimental implementation in detail, which is comprised of newly developed drive electronics for generating the required voltages to operate RF trap and TOFMS, as well as control electronics for regulating RF outputs and synchronizing the TOFMS extraction.

The photodissociation cross-section of SrCl$^+$ is measured in the spectral range of 36000 -- 46000 cm$^{-1}$ using a modular time-of-flight mass spectrometer (TOF-MS). By irradiating a sample of trapped SrCl$^+$ molecular ions with a pulsed dye laser, X$^1Σ^+$ state molecular ions are electronically excited to the repulsive wall of the A$^1Π$ state, resulting in dissociation. Using the TOF-MS, the fragments are detected and the photodissociation cross-section is determined for a broad range of photon energies. Detailed $\textit{ab initio}$ calculations of the molecular potentials and spectroscopic constants are also performed and are found to be in good agreement with experiment. The spectroscopic constants for SrCl$^+$ are also compared to those of another alkaline earth chalcogen, BaCl$^+$, in order to highlight structural differences between the two molecular ions. This work represents the first spectroscopy and $\textit{ab initio}$ calculations of SrCl$^+$.

Mass spectrometry is used in a wide range of scientific disciplines including proteomics, pharmaceutics, forensics, and fundamental physics and chemistry. Given this ubiquity, there is a worldwide effort to improve the efficiency and resolution of mass spectrometers. However, the performance of all techniques is ultimately limited by the initial phase-space distribution of the molecules being analyzed. Here, we dramatically reduce the width of this initial phase-space distribution by sympathetically cooling the input molecules with laser-cooled, co-trapped atomic ions, improving both the mass resolution and detection efficiency of a time-of-flight mass spectrometer by over an order of magnitude. Detailed molecular dynamics simulations verify the technique and aid with evaluating its effectiveness. Our technique appears to be applicable to other types of mass spectrometers.

A single ion immersed in a neutral buffer gas is studied. An analytical model is developed that gives a complete description of the dynamics and steady-state properties of the ions. An extension of this model, using techniques borrowed from the mathematics of finance, is used to explain the recent observation of non-Maxwellian statistics for these systems. Taken together, these results offer an explanation of the longstanding issues associated with sympathetic cooling of an ion by a neutral buffer gas.

Samples of ultracold 174 Yb+ ions, confined in a linear radio-frequency Paul trap, are heated via self-induced micromotion interruption, while their temperature, density, and therefore structural phase are monitored and simulated. The observed time evolution of the ion temperature is compared to a theoretical model for ion-ion heating allowing a direct measurement of the Coulomb logarithm in a linear Paul trap. This result permits a simple, yet accurate, analytical description of ion cloud thermodynamic properties, e.g. density, temperature, and structural phase, as well as suggests limits to and improvements for on-going trapped-ion quantum information efforts.

The role of electronic excitation in charge exchange chemical reactions between ultracold Ca atoms and Ba$^+$ ions, confined in a hybrid trap, is studied. This prototypical system is energetically precluded from reacting in its ground state, allowing a particularly simple interpretation of the influence of electronic excitation. It is found that while electronic excitation of the ion can critically influence the chemical reaction rate, electronic excitation of the neutral atom is less important. It is also experimentally demonstrated that with the correct choice of the atom-ion pair, it is possible to mitigate the unwanted effects of these chemical reactions in ultracold atom-ion environments, marking an important step towards the next generation of hybrid devices.

We demonstrate the implementation of a simple time-of-flight (ToF) mass spectrometer with medium-mass resolution ($m/Δm\sim50$) geared towards the demands of atomic, molecular, and chemical physics experiments. By utilizing a novel radial ion extraction scheme from a linear quadrupole trap, a device with large trap capacity and high optical access is realized without sacrificing mass resolution. Here we describe the construction and implementation of the device as well as present representative ToF spectra. We conclude by demonstrating the flexibility of the device with proof-of-principle experiments that include the observation of molecular-ion photodissociation and the measurement of trapped-ion chemical reaction rates.

Interactions between cold ions and atoms have been proposed for use in implementing quantum gates\cite{Idziaszek2007}, probing quantum gases\cite{Sherkunov2009}, observing novel charge-transport dynamics\cite{Cote2000}, and sympathetically cooling atomic and molecular systems which cannot be laser cooled\cite{Smith2005,Hudson2009}. Furthermore, the chemistry between cold ions and atoms is foundational to issues in modern astrophysics, including the formation of stars, planets, and interstellar clouds\cite{Smith1992}, the diffuse interstellar bands\cite{Reddy2010}, and the post-recombination epoch of the early universe\cite{Stancil1996b}. However, as pointed out in refs 9 and 10, both experimental data and a theoretical description of the ion-atom interaction at low temperatures, reached in these modern atomic physics experiments and the interstellar environment, are still largely missing. Here we observe a chemical reaction between ultracold $^{174}$Yb$^+$ ions and $^{40}$Ca atoms held in a hybrid trap. We measure, and theoretically reproduce, a chemical reaction rate constant of $ \rm \bf K =(2\pm1.3)\times10^{-10} cm^{3}s^{-1}$ for $ \rm \bf 1 mK \leq T \leq 10 K$, four orders of magnitude higher than reported for other heteronuclear cases. We also offer a possible explanation for the apparent contradiction between typical theoretical predictions and measurements of the radiative association process in this and other systems.

The formation of $^{40}$Ca$_2^+$ molecular ions is observed in a hybrid $^{40}$Ca magneto-optical and ion trap system. The molecular ion formation process is determined to be two-photon photo-associative ionization of ultracold $^{40}$Ca atoms. A lower bound for the two-body, two-photon rate constant is found to be $\barβ \geq 2 \pm 1 \times 10^{-15}$ cm$^{3}$ Hz. $\textit{Ab initio}$ molecular potential curves are calculated for the neutral Ca$_2$ and ionic Ca$_2^+$ molecules and used in a model that identifies the photo-associative ionization pathway. As this technique does not require a separate photo-association laser, it could find use as a simple, robust method for producing ultracold, state-selected molecular ions.

We demonstrate a simple technique for molecular ion spectroscopy. BaCl$^+$ molecular ions are trapped in a linear Paul trap in the presence of a room-temperature He buffer gas and photodissociated by driving an electronic transition from the ground X$^1Σ^+$ state to the repulsive wall of the A$^1Π$ state. The photodissociation spectrum is recorded by monitoring the induced trap loss of BaCl$^+$ ions as a function of excitation wavelength. Accurate molecular potentials and spectroscopic constants are determined. Comparison of the theoretical photodissociation cross-sections with the measurement shows excellent agreement. This study represents the first spectroscopic data for BaCl$^+$ and an important step towards the production of ultracold ground-state molecular ions.