Precision Measurement with Polyatomic Molecules

Polyatomic molecule uniquely enable the simultaneous combination of multiple features advantageous for precision measurement. Searches for charge-parity (CP) violation benefit from large internal molecular fields, high polarizability, internal co-magnetometry, and the ability to cycle photons - all of which can be found in certain polyatomic species. We discuss experimental and theoretical developments in several linear metal hydroxide (MOH) species. These include spectroscopic mapping of EDM-sensitive states, new spectroscopic methods for transitions relevant to laser cooling, photon cycling in species with complex hyperfine structure, and the demonstration of a "pathfinder" EDM experiment with ultracold and trapped polyatomics. We discuss how polyatomic structure gives rise to unique capabilities, such as the existince of EDM-sensitive yet field-insensitive measurement schemes. We also discuss progress towards extending these methods to species with short-lived nuclei, more complex ligands, and other advantageous features for precision measurement.