Zeeman interaction in ThO H^3Δ_1 for the electron electric-dipole-moment search

The current limit on the electron's electric dipole moment, ∣d_e∣ < 8.7 × 10^(−29) e cm (90% confidence), was set using the molecule thorium monoxide (ThO) in the J = 1 rotational level of its H^3Δ_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 Ω-doublet structure. These systematics can be further suppressed by operating the experiment under conditions where the g-factor difference between the Ω doublets is minimized. We consider the g factors of the ThO H^3Δ_1 state both experimentally and theoretically, including dependence on Ω 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 Ω 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