Using a three-path contrast interferometer (CI) geometry and laser-pulse diffraction gratings, we create a matter-wave interferometer with ytterbium (Yb) atoms. We present advances in contrast interferometry relevant to high-precision measurements. By comparing to a traditional atom interferometer, we demonstrate the immunity of the CI to vibrations for long interaction times (
>20ms). We characterize and demonstrate control over the two largest systematic effects for a high-precision measurement of the fine-structure constant via photon recoil with our interferometer: diffraction phases and atomic interactions. Diffraction phases are an important systematic for most interferometers using large-momentum transfer beam splitters; atomic interactions are a key concern for any Bose-Einstein condensate (BEC) interferometer. Finally, we consider the prospects for a future subpart per billion photon recoil measurement using a Yb CI.
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
2.5times106 radians of phase. We also demonstrate an interferometer with a statistical uncertainty of
deltaalpha/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.