Atom interferometry is a powerful metrological tool that has been developed over the last few decades. Large momentum transfer (LMT) methodsmanipulate atomic trajectories with tens or hundreds of photon momenta in order to increase sensitivity. This thesis furthers progress towards using LMT methods in next-generation atom interferometers. One main result establishes symmetric Bloch oscillations as a new, viable technique for LMT. Theory and numerics are used to show how the process is coherent and adiabatic, and experimentally we demonstrate coherence in an interferometer with up to 240¯hk, where ¯hk is the momentum of a single photon of 852nm light. This was the second largest coherent momentum splitting demonstrated at at the time of publication. The rest of the thesis focuses on design and construction of a new atomic fountain to measure the fine structure constant α. Discrepancies in recent measurements of α [67, 55] are currently limiting theory predictions for the electron gyromagnetic ratio [25] - an improved measurement of α is therefore highly motivated and would enable an improved test of the consistency of the Standard Model. Previously, our group published a measurement of α at the 0.2 ppb level in 2018 [67]. We built a new experiment with a goal of improving the measurement by a factor of 3-10. Much of the thesis focuses on systematic effects related to spatial intensity inhomogeneities on the laser beam, which are some of the hardest to characterize systematic effects looking forward. A large clear aperture vacuum chamber accommodates larger waist laser beams without clipping on chamber walls. In addition, a high-speed, user-friendly Monte Carlo simulation package was made to predict experimental systematic shifts in the measured value of α due to laser beam inhomogeneities.

The fine-structure constant $\alpha$ is ubiquitous in physics, and a comparison among different experiments provides a powerful test of the Standard Model of particle physics. We have recorded the most accurate measurement of $\alpha = 1/137.035999046(27)$ at an accuracy of 0.20 parts per billion (ppb) via measuring $h/m_\text{Cs}$, the quotient of the Planck constant and the mass of a cesium-133 atom. Our tools are simultaneous conjugate Ramsey-Bord e atom interferometers based on a cesium atomic fountain. Using Bragg diffraction and Bloch oscillations, we have demonstrated the largest phase (12 million radians) of any Ramsey-Bord e interferometer and controlled the systematic effects at a level of 0.12 ppb. Comparing the Penning trap measurements with the Standard Model prediction of the electron gyromagnetic moment anomaly $a_e$ based on our $\alpha$ result, a 2.5-$\sigma$ tension has been observed. This tension provides hints for new physics beyond the Standard Model.

One of the largest systematic effects of our $\alpha$ measurement comes from the gravity gradient $\gamma$. In order to suppress this effect in the next-generation $\alpha$ measurement, we have demonstrated a new atom interferometer configuration - offset simultaneous conjugate interferometers (OSCIs). We create two pairs of simultaneous conjugate interferometers and precisely control the offset between them with Bragg diffraction and Bloch oscillations. The multichannel readouts of OSCIs allow us to not only cancel the effect of $\gamma$, but also reduce the undesired diffraction phase from Bragg diffraction beam splitters.

Other ongoing and planned upgrades of the next-generation $\alpha$ measurement have also been presented in this thesis, including an over-sized vacuum chamber and a high-power pulsed laser system. With these upgrades, we expect to improve the accuracy of $\alpha$ by one to two orders of magnitude.

An atom interferometer offers means to measure physical constants and physical quantities with a high precision, with relatively low cost and convenience as a table-top experiment. A precision measurement of a gravitational acceleration can test fundamental physics concepts such as Einstein equivalence principle (EEP). We identified that the two lithium isotopes (${}^{7}$Li and ${}^{6}$Li) have an advantage for the test of EEP, according to the standard model extension (SME). We aim to build the world's first lithium atom interferometer and test the Einstein equivalence principle.\

We demonstrate a new laser cooling method suitable for a lithium atom interferometer. Although lithium is often used in ultra-cold atom experiments for its interesting physical properties and measurement feasibility, it is more difficult to laser cool lithium than other alkali atoms due to its unresolved hyperfine states, light mass (large recoil velocity) and high temperature from the oven. Typically, standard laser cooling techniques such as Zeeman slowers and magneto-optical traps are used to cool lithium atoms to about 1 mK, and the evaporative cooling method is used to cool lithium atoms to a few $\mu$K for Bose-Einstein condensate (BEC) experiments. However, for the atom interferometry purpose, the evaporative cooling method is not ideal for several reasons: First, its cooling efficiency is so low (0.01 \% or less) that typically only $10^4-10^5$ atoms are left after cooling when one begins with $10^9$ atoms. More atoms in an atom interferometer are needed to have a better signal to noise ratio. Second, an evaporative cooling is used to make a BEC, but we do not need a BEC to make an atom interferometer. In an atom interferometer, a high density of atoms as in a BEC should be avoided since it causes a phase shift due to atom interactions. Third, a setup for an evaporative cooling requires intricate RF generating coils or a high power laser. \

With a simple optical lattice and a moderate laser power (100 mW), we achieved a sub-Doppler cooling of lithium by a new laser cooling method despite the fact that lithium has un-resolved hyperfine structure. We identified that the Sisyphus cooling and the adiabatic cooling mechanisms cooperate and give both lower temperature and higher cooling efficiency than the result that can be achieved by each alone. We cooled ${}^{7}$Li atoms to $\sim \;50\;\mu$K (about 8 times the recoil temperature) in a one dimensional lattice with cooling efficiency of $50\%$. In three dimensions the cooling temperature was limited to $90\,\mu$K due to instability of our 3D lattice, however the same principle applies and potentially a lower temperature can be achieved in 3D as well.

Matter wave interferometry with laser pulses has become a powerful tool for precision measurement. Optical resonators, meanwhile, are an indispensable tool for control of laser beams. We have combined these two components, and built the first atom interferometer inside of an optical cavity. This apparatus was then used to examine interactions between atoms and a small, in-vacuum source mass. We measured the gravitational attraction to the source mass, making it the smallest source body ever probed gravitationally with an atom interferometer. Searching for additional forces due to screened fields, we tightened constraints on certain dark energy models by several orders of magnitude. Finally, we measured a novel force mediated by blackbody radiation for the first time.

Utilizing technical benefits of the cavity, we performed interferometry with adiabatic passage. This enabled new interferometer geometries, large momentum transfer, and interferometers with up to one hundred pulses. Performing a trapped interferometer to take advantage of the clean wavefronts within the optical cavity, we performed the longest duration spatially-separated atom interferometer to date: over ten seconds, after which the atomic wavefunction was coherently recombined and read out as interference to measure gravity. This work demonstrates the feasibility and utility of bringing a cavity to atom interferometry.

We experimentally and theoretically study Bragg diffraction as a tool for large-momentum transfer beam splitters in atom interferometry. A theoretical framework is developed to quantify the diffraction phase systematic caused by Bragg diffraction and experiments are performed to confirm these predictions using a Ramsey-Bord e atom interferometer. We then develop methods to systematically cancel and reduce the diffraction phase systematic by carefully selecting Bragg diffraction parameters and utilizing Bloch oscillations. These techniques are then applied to an ongoing precision measurement of $h/m_\text{Cs}$ for cesium, with the end goal of measuring the fine structure constant $\alpha$. We demonstrate a high contrast simultaneous conjugate Ramsey-Bord e interferometer using 5th order Bragg diffraction and 25 common mode Bloch oscillations which achieves $2.5\times 10^6$ radians of phase. We also demonstrate an interferometer with a statistical uncertainty of $\delta \alpha/\alpha=0.25$ ppb after 25 hours of integration time that has diffraction phase systematic error of around 1 ppb. Other sources of systematic uncertainty are also thoroughly explored and determined to better than 0.1 ppb. The techniques and theories developed in this thesis will hopefully help enable future precision measurements based on Bragg diffraction.

Atom interferometry deploys atoms as sensors, delivering precision measurements that span the gamut of physics. Laser-cooled samples simplify uniform detection strategies and allow meticulous control over degrees of freedom and systematic effects. Advanced cooling and interferometry techniques do apply readily to a few atomic species, but they leave behind a large class of species otherwise suited for precision sensing. This thesis describes atom interferometry with a sample of lukewarm $^7$Li, near the Doppler temperature. High thermal speeds demand rapid atom optics and complicate detection. We nevertheless develop interferometer techniques that considerably relax cooling requirements, including a recoil-sensitive scheme capable of measuring the fine-structure constant that takes advantage of $^7$Li's low mass. We also establish a phase-patterning protocol to inscribe and sense spatially-varying phases with matter-wave interferometers whose sample sizes exceed the arm separation. Phase patterning forms the basis of the first precision measurement of $^7$Li's red tune-out wavelength, the wavelength where AC Stark shifts from the $D$-line transitions cancel and the polarizability vanishes. Our measurement registers a 3-$\sigma$ tension with \emph{ab initio} atomic theory regarding the tensor-shifted tune-out wavelength and a 2-$\sigma$ tension regarding the size of the tensor shift, but agrees with theory regarding the scalar tune-out wavelength. These results motivate further work on lithium's polarizability, enable direct measurements of hyperpolarizability, and empower an assortment of future applications of phase patterning in matter-wave interferometry.

Low image contrast is a major limitation in transmission electron microscopy, since sampleswith low atomic number only weakly phase-modulate the illuminating electron beam, and beam-induced sample damage limits the usable electron dose. The contrast can be increased by converting the electron beam’s phase modulation into amplitude modulation using a phase plate, a device that applies a π/2 radian phase shift to part of the electron beam after it has passed through the sample. Previous phase plate designs rely on material placed in or near the electron beam to provide this phase shift. This results in image aberrations, an inconsistent time-varying phase shift, and resolution loss when the electron beam charges, damages, or is scattered from the material.

In this thesis, I present the theory, design, and implementation of the laser phase plate,which instead uses a focused continuous-wave laser beam to phase shift the electron beam. A near-concentric Fabry-Perot optical cavity focuses and resonantly enhances the power of the laser beam in order to achieve the high intensity required to provide the phase shift. We demonstrate that the cavity can surpass this requirement and generate a record-high continuous-wave laser intensity of 590GW/cm^2. By integrating the cavity into a transmission electron microscope, we show that the ponderomotive potential of the laser beam applies a spatially selective phase shift to the electron beam. This enables us to make the first experimental observation of the relativistic reversal of the ponderomotive potential.

We then theoretically analyze the properties of the contrast transfer function generated bythe laser phase plate. We experimentally determine that resolution loss caused by thermal magnetic field noise emanating from electrically conductive materials in the cavity can be eliminated by designing the cavity with a sufficiently large electron beam aperture. Finally, we show that the laser phase plate provides a stable π/2 phase shift and concomitant contrast enhancement when imaging frozen hydrated biological macromolecules. We use these images to successfully determine the structure of the molecules. This demonstrates the laser phase plate as the first stable and lossless phase plate for transmission electron microscopy.

Light-pulse atom interferometers have been used as quantum inertial sensors and for precision tests of fundamental laws of physics. For higher contrast, we apply conjugate Ramsey-Borde interferometers to cancel out vibrational noise and top mirror tilting to compensate the Coriolis force. For higher sensitivity, we implement Bragg diffraction and Bloch oscillations for large momentum transfer to increase the enclosed area of our atom interferometer. We also utilize Raman sideband cooling in our experimental setup, which increases the overall signal about twentyfold, and increases the contrast by suppressing the thermal expansion of the atom cloud.

By combining measurements of recoil frequency and a frequency comb, we present the first clock referenced to the mass of a single particle. The rest mass of a particle defines its Compton frequency, mc^2/h through relativity and quantum mechanics, and thereby sets a fundamental timescale. Our clock stabilizes a 10 MHz radio frequency signal to a certain fraction of the cesium Compton frequency. Future work could result in an elementary particle (electron) or even antimatter (antihydrogen) clock, opening up new ways to test CPT symmetry and the equivalence principle.

We also present our progress towards a new determination of the fine structure constant. The fine structure constant value obtained by our cesium Compton clock measurement is about three times better compared with the earlier cesium recoil frequency result. After combining Bragg diffraction and Bloch oscillations, we achieved 0.33 ppb sensitivity (0.66 ppb uncertainty of the recoil frequency measurement) in 6 hours, which is about two times better than the previous best recoil frequency measurement. The leading systematic effect is also reduced by a factor of 2.75.