Nuclear Spin Dependent Parity Violation in Diatomic Molecules

Nuclear spin-dependent parity violation (NSD-PV) effects arise from the exchange of the $Z^{0}$ boson between electrons and the nucleus and from the interaction of electrons with the nuclear anapole moment, a parity-odd magnetic moment. The anapole moment grows~as $A^{2/3~}$of the nucleus,while the $Z^{0}$ coupling is independent of $A$. We study NSD-PV effects using diatomic molecules, where signals are dramatically amplified by bringing rotational levels of opposite parity close to degeneracy in a strong magnetic field. Using a Stark-interference technique, we measure the NSD-PV interaction matrix element. We present results that demonstrate statistical sensitivity to NSD-PV effects surpassing that of any previous atomic parity violation measurement, using the test system~$^{\mathrm{138}}$Ba$^{\mathrm{19}}$F. We also discuss improvements on investigations of systematics due to non-reversing stray $E$-fields, $E_{nr}$~together with~$B$-field inhomogeneities, and short-term prospects for measuring the nuclear anapole moment of $^{\mathrm{137}}$Ba. In the long term, our technique is sufficiently general and sensitive to enable measurements across a broad range of nuclei.