This dissertation reports on precision measurements of the atomic structure of calcium ions (⁴⁰Ca⁺), application of trapped ⁴⁰Ca⁺ ions as a probe for a violation of fundamental symmetry and prospects of performing quantum simulations with trapped ion.

We demonstrate a novel technique to perform spectroscopy on the dipole transition of ⁴⁰Ca⁺ that circumvents usual difficulties from dark resonances and Doppler heating. The center of the atomic transition can be detected to a precision of 200 kHz or less with an integration time of 10 minutes. We apply this method to directly measure the influence of micromotion on the fluorescence spectra and confirm the dependence of the modulation index on the radial trap frequency.

We measure the branching fraction of the excited ²P_1/2 state of ⁴⁰Ca⁺ to be 0.93565(7) using a simple experimental scheme readily applicable to many other ion species. Our result for ⁴⁰Ca⁺ distinguishes well among various theoretically calculated values, which is important in guiding further developments of the theoretical work.

We apply the Ramsey spectroscopy technique based on a pair of correlated ions to probe the effect of the violation of local Lorentz invariance (LLI). The energy difference between the two components of the Bell state |Psi_B> = |m_J=5/2,m_J=-5/2>+|m_J=1/2,m_J=-1/2> in the D_5/2 manifold of ⁴⁰Ca⁺ is monitored for 12 hours. We found that the energy component related to the violation of LLI varies less than 17±22 mHz. Assuming a hydrogen-like model of ⁴⁰Ca⁺, the measurement result provides us the bound of the LLI parameter C⁽²⁾₀ to be 1.7±2.2x10^-17.

Based on numerical simulations, we show that the Aubry transition in the Frenkel-Kontorova model with trapped ion can be observed for practical experimental parameters such as the strength and wavelength of the optical lattice, which serves as an external perturbing periodic potential. Moreover, we also show that the normal mode structure of ion chain can change significantly as we vary the strength of the optical lattice.

Electric-field noise is a major limiting factor in the performance of ion traps and other quantum devices. Despite intensive research over the past decade, the nature and cause of electric field noise near surfaces is not well understood. This dissertation reports the high- temperature dependence of electric-field noise above an Al-Cu surface using a trapped 40Ca+ ion as a probe.

We employ a novel setup with a surface ion trap mounted on a heater for studies of the temperature dependence of electric-field noise. To characterize the Al-Cu material, we explore the effects of heat treatment through ex situ annealing followed by inspection in a scanning electron microscope. To calibrate the temperature of the trap, we demonstrate the use of thermal imaging for monitoring the temperature of an ion trap in vacuum.

The temperature and frequency dependence of electric-field noise above the surface is measured using the heating rate of a single ion in a surface-electrode Paul trap. We find that the heating rate saturates at temperatures greater than 450 K. We find that the frequency dependence shows a 1/f behavior, and has a lower frequency scaling exponent at high temperatures than at room temperature. We show that these results are a reflection of the surface-related noise by eliminating other possible sources of noise.

Building on historical data for resistance fluctuations in thin films, we develop the thermally-activated fluctuator model to describe the results. We find that a broad distribution of fluctuators with energy barriers peaked around 0.5 eV accurately models both the temperature and frequency dependence of the electric-field noise measured. We present the interpretation of this model as a way to infer that the cause of electric-field noise in the trap is likely defect motion in the metal surface, connecting the problems faced in ion trapping to a large body of work in solid state physics.

We present the results of an experiment that used the quantized motion of an ion trappedin a harmonic pseudopotential to test for nonlinear extensions of quantum mechanics. This test was motivated by the development of a recent, consistent theory of nonlinear quantum mechanics that, in contrast to previous frameworks, also preserves causality. This experiment represents the first test of this new theory in a fully quantum system and improved the bounds on potential nonlinear effects in quantum mechanics inferred from previous experimental results by an estimated eight orders of magnitude.

We also present the results of an experiment that used two entangled ions to test for localviolations of Lorentz invariance and which tightened the bound on such hypothetical violations by about half of an order of magnitude. In particular, this experiment used a special entangled state of the ions, residing within a decoherence free subspace, which is immune to the dominant source of noise. By comparing our results against a similar experiment, performed with two non-entangled ions, we verify the expected factor-of-two improvement in the signal-to-noise ratio predicted by theory. This improvement can be directly attributed to the use of entanglement and, thus, this work provides a case study of how entanglement can be leveraged as a resource to fundamentally enhance the performance of spectroscopic measurements

This work presents the techniques used to create a freely rotating trapped-ion Coulomb crystal and to establish quantum coherent control over this rotational motion. This is done using a highly symmetric surface ion trap with circular trapping electrodes. We derive how a trapped-ion rotor couples to coherent laser light, including the motional transition sideband spectrum and the corresponding coupling strengths. We also show how rotational motion modifies the coupling of the usual trapped-ion vibrational motion to laser light. In our experiments, light which is coupled to the rotor's motion propagates nearly normal to the trap surface, which is thus also sensitive to vibrational motion in this direction. We thus also present the design of and benchmark the performance of a Faraday cage which has successfully protected this motion from harmful electric field noise.

A prerequisite to clean, coherent manipulation of the rotational quantum state of our rotor is preparing it in a rapidly rotating state with a small uncertainty in its angular momentum. This rotational state preparation is done with by accelerating a rotating quadrupole field via time-dependent voltages applied directly to the trap electrodes, resulting in rotation frequencies of 100's of kHz with uncertainties within 1 kHz. We show how this procedure allows for creation of superpositions of angular momentum states, and present considerations and measurements pertaining to optimizing this procedure. We find that the coherence of these superpositions is limited by angular momentum diffusion processes induced by coupling to noisy electric field gradients. Careful measurements of these rotor decoherence dynamics demonstrate close agreement with the corresponding theory for the first time.

Finally, we present a proposal to use angular momentum superpositions of our trapped ion rotor as an interferometer in which we may exchange the positions of two ions. This experiment would serve as a test of the symmetrization of their mutual quantum state, and would be sensitive to the phase of the exchange operation without requiring the two particles to coincide spatially. We interpret the physical meaning of this exchange phase measurement and present detailed considerations of potential errors.

We present experimental results of using trapped ions for the study of energy transport and quantum correlations in many-body systems. We investigate energy propagation by locally exciting one end of an ion chain and then observing the subsequent dynamics. The experimental results agree with the presented normal mode model of ion motion, and signify the first steps towards realizing theoretical proposals of studying many-body physics with the motional degree of freedom of trapped ions. Additionally, we present a method for detecting correlations between an open quantum system and its environment by acting only locally on the open system. We implement this method using a single trapped ion and discuss our current work towards extending the results to larger systems. Lastly, we demonstrate how the presented method for local detection of quantum correlations can be used for detection of quantum phase transitions.

In this work, we present the design, fabrication, and operation of a novel surface-electrode Paul trap that produces a radio-frequency-null along the axis perpendicular to the trap surface. This arrangement enables control of the vertical trapping potential and consequentially the ion-electrode distance via dc-electrodes only. We demonstrate confinement of single 40Ca+ ions at heights between 50 μm and 300 μm above planar copper-coated aluminum electrodes. Laser-cooling and coherent operations are performed on both the planar and vertical motional modes. This architecture provides a platform for precision electric-field noise detection, trapping of vertical ion strings without excess micromotion, and may have applications for scalable quantum computers with surface ion traps.In our novel surface trap, we probe electric-field noise for ion-surface distances d between 50 μm and 300 μm in the normal and planar directions. We find the noise distance dependence to scale as d^−2.6 in our trap and a frequency dependence which is consistent with 1/f noise. Simulations of the electric-field noise specific to our trap geometry provide evidence that we are not limited by technical noise sources. Our distance scaling data is consistent with a noise correlation length of about 100 μm at the trap surface, and we discuss how patch potentials of this size would be modified by the electrode geometry. Finally, we achieve coupling between the motions of trapped ions separated by 620 μm. Our results are marked by the implementation of remote ion-ion interactions enhanced via an electrically floating metallic wire in an RF Paul trap. By tuning the confinement of each ion into resonance, we demonstrate classical energy exchange through sympathetic heating and heating rate reduction. The coupling interaction exchange time is extracted to be 22 ms. Practical improvements to the ion-wire-ion system are discussed, with realistic applications to sympathetic cooling of remote ions and more optimistic goals of coherent energy exchange at the single-quantum level. Our ion-wire-ion system establishes a building block for scalable trapped ion quantum computers and provides a tool for quantum communication between qubits of different types.

In this work, we present a novel method to couple any two vibrational modes of a single trapped ion, allowing energy to be swapped between the two modes. We use the scheme to perform ground state cooling and heating rate measurements of vibrational modes without direct optical access. This lessens experimental design constraints in trapped ion experi- ments, particularly in surface trap apparatus where optical access can be difficult.

We use a single ion as an electric-field noise sensor to study noise processes originating on the metallic surfaces of microfabricated ion traps. We show that realistic models of surface noise predict a specific polarization of the electric-field fluctuations relative to the trap geometry. In contrast, technical noise sources predict a different polarization direction and magnitude which can be inferred by electrostatic simulation of the trapping electrodes. We show that, by comparing heating rates of the two radial modes of a single trapped ion, one can determine whether technical noise sources are a significant contribution to heating. This is an important test for experiments aimed at studying surface noise effects. We also study dephasing due to surface noise, in which the electric potential curvature due to surface noise sources disturbs the phase of the ion motion. We measure the dephasing time for trapped ion motion. Using a noise model featuring dipolar noise sources, we probe the power spectrum of surface noise effects. These measurements, especially if repeated in a trap with smaller ion-electrode distances, may yield new insights as to the physical origin of surface noise effects.

We demonstrate a two-ion quantum simulation of vibrationally-assisted energy transfer, an important phenomenon in biochemical energy transfer. We show that the quantum simulator performs well when benchmarked against exact numerical simulation. We believe that our approach can be scaled to more complicated systems beyond the reach of classical simulation, and discuss several methods for extending the simulation.

In this thesis, I present the design, implementation, and characterization of a novel, rotationally symmetric ion trap. Our compact design creates a toroidal trapping potential for charged atoms that has a radius that is much smaller than the height at which the ions are positioned above the surface of the trap. We trap ions at a height of 385~$\mu$m and a radius of 45~$\mu$m as expected from simulation. We demonstrate that this ring is rotationally symmetric with imperfections in the potential of much less than 3~mK.

With two ions contained in a point Paul trap, we demonstrate the creation of a 100~kHz rotating ring using a rotating quadrupole. By releasing the quadrupole potential, we demonstrate the ability to create superpositions of rotational states using the modulation of the laser light produced by the classical rotation of the crystal in a symmetric potential. Superpositions of rotational states differing by up to four quanta are observed.

With these rotational superpositions, we describe an experiment capable of observing the identical nature of two ions in a Coulomb crystal. By creating a rotational interferometer, one can coherently exchange two particles and observe their interference upon recombination. We describe what this interference signature would be and how particle indistinguishability would affect it. We present experimental efforts towards realizing this exchange and reflect on our unexpectedly short rotational superposition coherence times.

In this dissertation, we present work on a quantum hybrid device comprising of a trapped calcium atom and a superconducting LC resonator. This hybrid device is a first step towards building a hybrid quantum computer that can take advantage of the different properties of atomic and superconducting quantum systems and combine the best characteristics of both. We model a trapped ion as an LC circuit and calculate its coupling to a mode of an LC resonator. Further, we optimize the trap geometry and placement of coupling electrodes to increase the coupling. We also outline the manufacturing process and simulation of the trapping potentials for the surface traps used in this work. Finally, we report on initial experiments coupling a trapped ion to a resonant mode of the LC resonator, increasing the heating rate to 220 phonons/ms on resonance versus 0.5 phonons/ms without additional heating from the resonator. The ratio of the heating rates for the two secular frequencies of the ion confrm our simulated coupling rates.

All surfaces generate electric-field noise, yet the physical origins of this noise are not well understood. This has been an active area of research in the ion trapping community for the past two decades, as ions are highly sensitive to electric-field fluctuations. With our work, we aim to illuminate the microscopic processes that drive charge dynamics on metal surfaces, so as to enable the engineering of low noise quantum devices.

We use single trapped calcium ions as detectors to study the 1/f noise generated by the surfaces of ion traps. We the study this noise by observing how it responds to changes in the properties of the trap surface. The surface properties are altered using treatments including prolonged heating, argon ion milling, and electron bombardment. In situ characterization tools are used to monitor the effects of these treatments. Our measurements are consistent with noise produced by an ensemble of thermally activated fluctuators, so our data is discussed in this context.

In this dissertation, we present results from a lengthy series of surface treatment experiments, the majority of which took place on a single aluminum-copper substrate. The results of these experiments indicate that argon ion milling can lower noise both by removing contaminants and by altering the morphology of the trap surface. The effects of morphology are isolated from the effects of contaminant removal via heat treatments, which alter the structure of the surface without changing its chemical composition. Through electron bombardment experiments, we begin an exploration of the relationship between hydrocarbon adsorbate structure and electric-field noise. In addition, we compare the noise characteristics of a set of similarly fabricated traps, and determine that atmosphere exposure has a major impact on noise produced by aluminum-copper films.

These experiments establish links between the electric-field noise characteristics and the microscopic properties of a contaminated metal trap surface. The insights we draw in this work can inform the next generation of ion trap engineering, storage, and treatment.