Statistics and systematics of electron EDM searches with BaF

The NL-$e$EDM experiment searches for a non-zero electric dipole moment of the electron $d_e$ ($e$EDM) in the ground state of barium monofluoride (BaF). A beam of BaF from a supersonic expansion source is probed with the spin precession method presented in \cite{Boeschoten2024}. This method permits the extraction of an $e$EDM value as well as values for parameters causing a possible systematic bias leading to a false $e$EDM. The currently achievable sensitivity is limited by statistics collected in a period of 34 hours and yields an $d_e$ of $2(3) \times 10^{-25}$ $e,$cm. Furthermore, from the same dataset sufficiently strong limits on parameters which can induce a false $e$EDM are extracted. These are mainly the electric field \textbf{E} and the intensity of the lasers fields in the fiducial volume of the experiment. We summarize the steps required to upgrade of the experiment to reach a competitive level on $d_e$, e.g. an intense laser-cooled beam from a cryogenic buffer gas source and the light collection efficiency of fluorescence.

💡 Research Summary

The NL‑eEDM collaboration reports on the first implementation of a search for a permanent electric dipole moment of the electron (eEDM) using ground‑state barium monofluoride (BaF) molecules. The experiment employs a supersonic expansion source to produce a cold, fast molecular beam (≈600 m s⁻¹, rotational temperature ≈3.5 K) and probes the beam with a novel spin‑precession technique introduced in Boeschoten et al. 2024.

In the spin‑precession method, a coherent superposition of the hyperfine states |F = 1, m_F = ±1⟩, |F = 1, m_F = 0⟩ and |F = 0, m_F = 0⟩ is created by a two‑photon Raman transition via the electronically excited A ²Π₁/₂ state. After a free evolution time T (typically 1–2 ms) in simultaneous electric (E) and magnetic (B) fields, a second Raman pulse projects the superposition back onto the population basis. The measured populations P₀ and P₁ depend on the accumulated phase ϕ = (2μ_B/ħ ± d_e P(E) W_d) T, where the sign of the eEDM contribution flips when the relative orientation of E and B is reversed. By alternating the field polarity and fitting the full optical‑Bloch‑equation model to the observed P₀(δ) spectra, the experiment extracts both the eEDM signal and a set of experimental parameters (detunings, Rabi frequencies, field strengths) that could otherwise generate systematic biases.

The statistical sensitivity of a molecular EDM experiment is given by

 δd_e = 1 /