This Dissertation details the development of state-of-the-art hybrid atom-ion trapping architecture and technique towards increasing the quantum control of matter and the detection of chemical processes at cold temperatures. Experimental work discussed herein is performed primarily using the second-generation of the MOTion trap, a hybrid atom-ion trap consisting of a co-located magneto-optical trap (MOT) and a linear quadrupole trap (LQT), with which $^{40}$Ca and a variety of atomic and molecular ions (Yb$^+$, Ba$^+$, BaCl$^+$, and others) can be co-trapped and cooled. Such a device enables the immersion of laser-cooled, ionic Coulomb crystals in diffuse gases of laser-cooled, highly-polarizable neutral atoms, allowing for studies in sympathetic cooling, cold atom-ion chemistry, and nonequilbrium collisional dynamics.

In the first of these studies, I discuss our method of sympathetic cooling in which we use a laser-cooled gas of Ca atoms to sympathetically cool BaCl$^+$ ions confined in the LQT. Because of the large polarizability of Ca, this method is found to be extremely efficient at cooling the notoriously difficult vibrational degree of freedom. This technique opens the door to research with general, ultracold, highly-localized molecular ions in the quantum ground-state which are not able to be produced using the more traditional methods of Doppler-cooling or photoassociation.

In the study of cold chemistry in the hybrid trap, I characterize a fundamental reaction, known as charge exchange, at the single-particle level in which an electron is transferred from a neutral atom to an atomic ion during an inelastic collision. This low-temperature process is thought to be foundational to the chemistry leading to the formation of stars, planets and interstellar clouds in our universe. Herein I discuss how improved experimental architecture has enabled the determination of reaction rate constants for individual electronic states of the reactants.

Our theoretical study of the collisional processes in hybrid atom-ion traps has led to the discovery of surprising nonequilibrium physics which exists in the hybrid trap environment. Herein I outline the collisional dynamics between neutral atoms and atomic ions in the presence of a time-dependent confining potential and describe how these dynamics manifest themselves in the emergence of nonequilbrium phenomena as indicated by bifurcations in steady-state energies of trapped ions. I show how the these dynamics can potentially limit the efficiency and overall viability of using neutral buffer gases to sympathetically cool the translational motion of trapped ions to ultracold temperatures.

In addition to these experimental studies, the development of architecture is discussed with focus given to the implementation of a novel time-of-flight mass spectrometer (TOF-MS) for use with hybrid atom-ion traps as well as standard LQTs. This simple, modular device couples radially with the LQT and enables the straightforward mass analysis of trapped species without complications derived from typical experimental difficulties, engineering constraints, and financial concerns. With this robust device we precisely characterize chemical processes which can take place in these hybrid atom-ion traps. Additionally, I describe how this new architecture is used to perform the action spectroscopy of several previously unstudied molecular ions in order to further establish the field of cold molecular ion research and the widespread use of hybrid atom-ion traps.

$^{133}$Ba$^+$ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus, visible wavelength electronic transitions, and long D-state lifetimes ($\tau\sim $1~min). Using a microgram source of radioactive material, we trap and laser-cool the synthetic \textit{A} = 133 radioisotope of barium II ($\tau_{1/2} \approx 10.5$~yr) in a radio-frequency ion trap.

To demonstrate high fidelity qubit operations, a number of unknown state energies were needed. We measure the isotope shift and hyperfine structure of the 6$^2$P$_{1/2}\leftrightarrow 5^2$D$_{3/2}$ electronic transition needed for laser cooling, state preparation, and state detection of the clock-state hyperfine and optical qubits.

For high-fidelity operations with electron shelving, we report measurements of the 6$^2$P$_{3/2}$ and $5^2$D$_{5/2}$ hyperfine splittings, as well as the~6$^2$P$_{3/2}~\leftrightarrow~6^2$S$_{1/2}$ and ~6$^2$P$_{3/2}~\leftrightarrow~5^2$D$_{5/2}$ transition frequencies.

Using these transitions, we demonstrate high-fidelity \ba \ hyperfine qubit manipulation with electron shelving detection to benchmark qubit state preparation and measurement (SPAM). Using single-shot, threshold discrimination, we measure an average SPAM fidelity of $\mathcal{F} = 0.99971(3)$, a factor of $\approx$ 2 improvement over the best reported performance of any qubit.

Finally, we report the 6$^2$P$_{1/2}\leftrightarrow 5^2$D$_{3/2}$ electronic transition isotope shift for the rare \textit{A} = 130 and 132 barium nuclides, completing the spectroscopic characterization necessary for laser cooling all long-lived barium II isotopes.

Ultracold cold molecular ions promise new directions in various studies of fundamental physics, such as precision measurements, ultracold chemistry and quantum information sciences. All these exciting applications require the molecular ion to be prepared at ground state of motional and internal degrees of freedom. It has been proposed that this stringent goal could be achieved through sympa-thetic cooling via collisions with laser-cooled neutral atoms. Three fundamental

issues of this method are addressed in this thesis.

First, an analytical model is established to accurately describe collision-induced heating of a single ion in contact with cold neutral atoms. This model reveals that micromotion interruption is the cause of heating, and gives results about steady-state temperature and sympathetic cooling rate verified by Monte-Carlo simulations. It also provides insight into the power-law tails observed in the

energy distribution of the trapped ion.

Next, we consider the case of multiple ions, whose inter-particle Coulomb repulsion causes ions in the Coulomb crystal state to spontaneously melt into a gas phase ion cloud, due to the same micromotion interruption mechanism. The analysis of this problem with a plasma model leads to the experimental determination of a quantity central to plasma physics, Coulomb Logarithm, in an

ion trap.

Finally, we demonstrate a molecular ion spectroscopy technique through the example of trap-depletion photodissociation of BaCl + . Although not sensitive to rotational structure, this method already reveals much about the fundamental quantum physics in the photodissociation process. The measured cross-section results paves the road toward state-selective spectroscopy currently going on in our lab.

This dissertation presents a search for the low lying transition in the 229Th nucleus. This nucleus is expected to have an exceptionally low energy and long-lived isomeric level just above the ground state which could be amenable to laser spectroscopy. We utilize 229Th doped LiSrAlF6 crystals to achieve high densities adequate for broadband synchrotron excitation. The charge state of the doped thorium atoms (4+) ensures a radiative decay upon de-excitation of the nucleus, necessary for fluorescence detection. Additionally; we built a pulsed VUV laser system, utilizing four wave difference frequency mixing in Xe, to continue interrogation of the 229Th:LiSrAlF6 crystals with improved sensitivities to longer lifetimes for the decay from the isomeric level. And finally, we utilize a 233U source along with superconducting single photon nanowire detectors (SNSPD's) in attempt to measure the internal conversion (IC) decay channel available to neutral 229Th. If successful, the experiment can provide the lifetime of the IC decay and can potentially provide energy bounds on the isomeric level.

This dissertation focuses on observing and controlling cold atom-ion collisions. Such collisions have numerous applications ranging from providing insight into the formation of the interstellar medium to presenting a potential platform for developing quantum information architectures. The experimental apparatus at the center of this work is a hybrid atom-ion trapping system in which laser-cooled Ca atoms held within a magneto-optical trap are spatially overlapped with ions localized within an ion trap. The ions studied in this work are both laser-cooled atomic ions as well as sympathetically cooled molecular ions. As detailed in the remainder of this thesis, by employing tools such as optical pumping, collision energy control, and mass spectrometry, reactions between these species can not only be studied with high precision but can also be controlled, leading to expanded tools for reaction engineering as well as the creation of exotic chemical species. Finally, this work also includes efforts to use inelastic collisions between room temperature BaCl^+} molecular ions and cold Ca atoms to create ro-vibrational ground state molecules, a precursor for developing a high-fidelity qubit based on rotational levels in polar molecules.

Cold molecules represent a frontier in the field of physics. Optical cycling, a process allowing repeated absorption and emission of photons by a molecule without altering its internal state, is the key to trapping and cooling molecules, as well as to quantum manipulation. However, the search for these molecules faces challenges including identifying suitable species that exhibit the required closed transition pathways for efficient optical cycling. The complexity of molecular structures, such as the electronic, vibrational and rotational properties, presents substantial hurdles in advancing this domain. To better understand these molecular physical and chemical properties, we have been working on the optical cycling properties of many different molecules, ranging from diatomic molecular ions to large neutral molecules with mass >300 amu. The results suggest that many of these candidates could potentially be laser-cooled using just a few repumping lasers, although significant progress is still required.

This dissertation focuses on the search of optical cycling molecules by presenting comprehensive studies of a diatomic molecular ion (SiO+) and molecules with optical cycling centers (OCCs). Through detailed analysis utilizing molecular Hamiltonian and experimental approaches such as high-resolution laser spectroscopy and dispersed laser-induced fluorescence (DLIF) spectroscopy, we studied the key mechanisms underlying these molecules. This work elucidates the electronic, vibrational, and rotational structures essential for achieving efficient optical cycling, investigates how the non-Born-Oppenheimer (non-BO) effects, such as the Fermi resonance and Jahn-Teller effects, may affect the cycling properties. The findings of new molecular species, such as the large molecules like Ca/SrOPh-diadamantanes, offer new insights into the selection criteria for potential molecules. Our findings not only enriched the promising molecular systems for laser cooling and quantum state detection, but also provides a foundation for future exploration and application of these molecules in advancing quantum technologies and precision spectroscopy.

The 229mTh isomeric state holds much promise as the reference for a clock of incredi-bly high precision and accuracy. This dissertation discusses the first direct excitation of the 229Th isomer in a LiSrAlF6 environment, and the laser system that was used for excitation spectroscopy. In addition, we discuss two other efforts towards determina- tion of the energy of the isomeric transition. The first involved the implantation of 229mTh into a superconducting nanowire single-photon imager (SNSPI). The second was towards the first instance of laser-based conversion electron M¨ossbauer spec- troscopy (CEMS) in a ThO2 sample. The results of these efforts will be discussed, as well as possible improvements that would enable detection of the isomeric transition within these environments.

This dissertation details of the construction of and experiments performed in a hybrid system consisting of a cold neutral atomic magneto-optical trap (MOT) contained within a linear radio-frequency quadrupole ion trap (LQT). The combination of these two workhorses of atomic physics facilitates a variety of developing science such as the controlled investigation of ion-neutral quantum chemistry and the production of ground-state molecular ions. While the primary focus of this work is the production of ultracold molecular ions via sympathetic cooling, there has been investigation of cold (T ~ mK) ion-neutral charge exchange processes in two different ion-neutral pair systems. In addition, a possible method of producing ultracold homonuclear molecular ions via a photo-associative ionization (PAI) pathway is studied in the MOT. The LQT traps ions in spatial overlap with a ⁴⁰Ca MOT constituting an ultracold buffer gas purposed to sympathetically cool molecular ions.

An effective, general method of producing ground-state molecular ions would open a field of physics allowing, for example, precise measurements of molecular transitions which are uniquely sensitive to parity violation, or the possible variation of fundamental constants. Another promising application of cold molecular ions is an implementation of a quantum computing architecture by coupling micro-fabricated strip-line resonators to the microwave rotational transition found in many diatomic molecular ions. The molecular ion BaCl⁺ is chosen to be used in proof-of-principle sympathetic cooling experiments. Ultimately, a vibrational internal state thermometry experiment shows that the Ca MOT performs very efficiently at quenching the vibrational motion of the BaCl⁺ molecular ion.

As a product of overcoming experimental challenges, this thesis discusses several experiments to characterize trapping and reaction dynamics in the hybrid system. For example, charge transfer measurements are performed with two different laser-cooled atomic ion species, Yb⁺ and Ba⁺, which are allowed and disallowed ground-state reaction, respectively. Controlled measurements of these inelastic processes test the cutting edge of quantum theory of ion-neutral interaction in both the ground-state and under optical excitation.

This dissertation describes experiments performed in the MOTion trap, a hybrid atom--ion trap comprised of a magneto-optical trap (MOT) and a linear Paul trap with an integrated time-of-flight mass spectrometer (ToF-MS).We aim to sympathetically cool the vibrational and rotational degrees of freedom of a BaCl$^+$ molecular ion by overlapping a cold ($\sim4$~mK) Ca MOT. This sympathetic cooling can prepare a molecular ion in its rovibrational quantum ground state, providing a method for state preparation for applications in molecular ion quantum logic. While collisions between the molecular ion and the cold atoms can cool the internal degrees of freedom, chemical reactions are also possible for electronically excited atoms. As such, we study these excited-state atom--ion reactions at low temperature $<1$~K and develop tools to control these collisions. We make the first experimental observation of reaction blockading, an effect that suppresses excited-state reactions at low temperature, and develop a method to reverse this suppression if desired with the addition of a catalyst laser, providing a means to optically control such reactions.

Beyond its intended purpose of studying and achieving sympathetic cooling, we find that this apparatus is a powerful tool for chemical studies.By imaging the ions, we can observe reactions occurring one atom at a time. We can precisely tune the collision energy or temperature down to the mK regime to as high as $\sim$10~K using techniques described in this dissertation, allowing controlled interrogation of these low-temperature reactions. Further, using lasers to address electronic transitions, we can precisely control the quantum state of the reactants, and we can measure the reaction products with the ToF-MS. A testament to the value of this apparatus is the study of BaOCa$^+$ described in this dissertation. Using the tools of the MOTion trap, we were able to identify the production of BaOCa$^+$, the first observation of a mixed hypermetallic oxide, and determine the path of reaction as BaOCH$_3^+$ + Ca($4s4p$~$^3P_J$) $\rightarrow$ BaOCa$^+$ + CH$_3$.

In addition to developing control of these atom--ion interactions towards sympathetic cooling of molecular ions, we also work towards further developing new quantum logic schemes for molecular ions, such as dipolar quantum logic, dipole--phonon quantum logic (DPQL), and electric-field gradient gates (EGGs).Specifically, we propose a class of molecules particularly well-suited for DPQL, the alkaline earth monoxide cations, that can also be added to existing atomic ion experiments with minimal additional experimental complexity. We further develop the techniques for DPQL and propose methods for single- and two-qubit gates, outlining a path towards universal quantum computation with molecular ions.