A novel spectroscopic design toward the measurement of electron's electric dipole moment using lead monofluoride

The search for the electron's electric dipole moment (eEDM) has long been pursued to explore the new physics beyond the Standard Model. To date, the most stringent constraints on the eEDM measurement were imposed by paramagnetic polar diatomic molecules/molecular ions through probing the changes of the precession rate of electron spins in an electric field, although nonzero eEDM has not been reported yet. In this study, we propose a novel design of spectroscopic detection in the lead monofluoride (²⁰⁸Pb¹⁹F) molecule that can take full advantage of its long coherent ground state, low Landé g factor, strong internal electric field, and unique field-dependent eEDM sensitive transition. Adopting an effective Hamiltonian approach, we untangle the complicated J-mixing energy level structure of the coherent ground state X₁²Π_1/2(υ = 0, J = 1/2, e, F = 1, |M_F| = 1), and characterize the rotational branching ratios in the A²Σ_1/2(υ′ = 0) ← X₁²Π_1/2(υ = 0) detection scheme. We demonstrate the highly asymmetric branching ratios in the Σ←Π transition which permits the preparation of coherently mixed states, followed by the simulated Stark spectroscopy under the externally applied electric field to address the sensitive transition Q_fe(1/2) for the eEDM measurement. In the end, we discuss the feasibility of laser cooling and Stark deceleration of PbF molecules. Our detection scheme will support us in constructing a fully optical approach toward the eEDM measurement using PbF molecules, which can enrich the molecular pool that explores the fundamental physics on a table-top apparatus.