Zeeman Interaction In Tho H-3 Delta(1) For The Electron Electric-Dipole-Moment Search

The current limit on the electron's electric dipole moment, vertical bar de vertical bar < 8.7 x 10(-29) e cm (90% confidence), was set using the molecule thorium monoxide (ThO) in the J = 1 rotational level of its H-3 Delta(1) electronic state [J. Baron et al., Science 343, 269 (2014)]. This state in ThO is very robust against systematic errors related to magnetic fields or geometric phases, due in part to its Omega-doublet structure. These systematics can be further suppressed by operating the experiment under conditions where the g-factor difference between the Omega doublets is minimized. We consider the g factors of the ThO H-3 Delta(1) state both experimentally and theoretically, including dependence on Omega doublets, the rotational level, and the external electric field. The calculated and measured values are in good agreement. We find that the g-factor difference between Omega doublets is smaller in J = 2 than in J = 1 and reaches zero at an experimentally accessible electric field. This means that the H, J = 2 state should be even more robust against a number of systematic errors compared to H, J = 1.