Magnetic and electric dipole moments of the $H$ ${}^3{\Delta }_1$ state in ThO

The metastable $H{}^3{\Delta }_1$ state in the thorium monoxide (ThO) molecule is highly sensitive to the presence of a $CP$-violating permanent electric dipole moment of the electron (eEDM) [E. R. Meyer and J. L. Bohn, Phys. Rev. A 78, 010502 (2008)]. The magnetic dipole moment ${\mu }_H$ and the molecule-fixed electric dipole moment $D_H$ of this state are measured in preparation for a search for the eEDM. The small magnetic moment ${\mu }_H=8.5\left(5\right)\times {10}^{-3}{\mu }_B$ displays the predicted cancellation of spin and orbital contributions in a ${}^3{\Delta }_1$ paramagnetic molecular state, providing a significant advantage for the suppression of magnetic field noise and related systematic effects in the eEDM search. In addition, the induced electric dipole moment is shown to be fully saturated in very modest electric fields (<10 V/cm). This feature is favorable for the suppression of many other potential systematic errors in the ThO eEDM search experiment.

Figure 1

(a) The magnet assembly used in the measurement of ${\mu }_H$. Arrows on the NdFeB magnets indicate the direction of magnetization. (b) The $\widehat{z}$ component of the $\mathcal{B}$ field, ${\mathcal{B}}_z$, measured along the $x$ axis. The shaded area indicates the calculated acceptance of the LIF detection optics. (c) Measured (red squares) and calculated (solid green line) values of ${\mathcal{B}}_z$ along the $y$ axis. The shaded area indicates the LIF excitation region, defined by the probe laser's intensity profile.

Figure 2

Spectra of LIF from the $H,J=1$ state in a magnetic field $\mathcal{B}$ $=$ 1.9(1) kG, acquired with 16 averages per data point. The $x$-error bars account for the standard error in the laser's frequency offset (derived from the rms frequency excursion of the lock's error signal). The $y$-error bars indicate the quadrature sum of the standard error of the LIF signal due to shot-to-shot fluctuations in the yield of molecules in a pulse, and the $y$-error derived from the $x$-error bars using the numerically calculated slope of the data. (a) The probe laser's polarization $\widehat{\epsilon }\parallel \vec{\mathcal{B}}$; in this configuration the $m_J=0$ sublevel is probed. (b) With the laser polarization $\widehat{\epsilon }\perp \vec{\mathcal{B}}$, the $m_J=\pm 1$ sublevels are probed. The fit to the spectrum in (b) yields $\Delta {\nu }_{\pm }$ $=$ 22.66(41) MHz for the Zeeman splitting between $m_J=\pm 1$.

Figure 3

(a) LIF spectrum from the $H,J=1$ state in an electric field $\mathcal{E}=20$ V/cm, acquired with 16 averages per data point. The error bars are assigned in the same way as in Fig. 2. The two $\mathcal{E}$-field-polarized states are separated by a frequency $\Delta$. The LIF signal near zero offset is due to molecules outside the electric field plates (see text). In (b), $\Delta$ is plotted as a function of the $\mathcal{E}$ field across the plates. The solid line is a fit to the function $\Delta =|D_J\mathcal{E}|$. The slope of the plot yields $D_{J=1}=h\times 2.13\left(2\right)$ MHz/(V/cm) for the dipole matrix element between the $\Omega$-doublets in $H,v=0,J=1$ state.