Atom interferometry has allowed for some of the most precise measurements in physics and has found broad applicability. Despite this, interferometry with ultracold ions is essentially non-existent. I will present current work at UCLA to perform precision rotation sensing via matter-wave interferometry of a single trapped ion [1,2]. To do this, we harness the recently developed technique of ultrafast ‘State-Dependent Kicks’ . Splitting the atom in a few trillionths of a second provides a way to build a robust, sensitive ion gyroscope. Similar techniques are also being investigated in neutral atom interferometers and I will discuss how further ion interferometry applications could be developed that afford long coherence times in a compact apparatus. I will also describe how ultrafast manipulations offer a paradigm shift in trapped-ion quantum computing, and how our work paves the way for high speed, high fidelity operations. Finally, I will outline ideas for utilizing trapped ions for testing foundational questions in quantum mechanics.
 J. Phys. B 50, 064002 (2017)
 Phys. Rev. A 100, 063622 (2019)
 Phys. Rev. Lett. 110, 203001 (2013)