Probing $P,T$-Symmetry Violation with Optically Trapped Asymmetric Top Molecules
Searches for $P,T$-violating electromagnetic moments are among the most sensitive probes of physics beyond the Standard Model. Extending beyond current limits will benefit from molecules with fully controllable orientation at low electric fields, long coherence times, and laser coolability---all offered by asymmetric top molecules (ATMs). Exploiting the intrinsic rotational $K$-doubling in ATMs and the associated long-lived ($T_1 \gtrsim 10$ s) parity doublets afforded by $C_{2v}$ symmetry and nuclear-spin statistics, these species combine large electric polarizability with long coherence times in modest laboratory fields. We study alkaline-earth(-like) monoamides, $\mathcal{M}$--NH$_2$ ($\mathcal{M}$ = Ca, Sr, Ba, Yb, Ra), which possess favorable electronic structure for laser cooling. We perform \textit{ab initio} calculations of fine and hyperfine constants, identifying the importance of relativistic effects in the spin-rotation tensor. An effective Hamiltonian then models the rotational and hyperfine structure of the vibronic ground state, quantifying electron electric dipole moment (EDM) sensitivities and identifying feasible measurement schemes. We compute the effect of external fields and identify engineered clock transitions that suppress sensitivity to external perturbations while retaining strong EDM sensitivity, and characterize the magic trapping conditions that null differential light shifts in an optical trap. Under these conditions we project a statistical electron-EDM sensitivity over an order of magnitude beyond current best experimental limits, with further gains available from increased molecule number and coherence time. Our results establish asymmetric top molecules as a tunable platform for sensitive symmetry-violation measurements with long coherence times.