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Nuclear spin-dependent parity violation (NSD-PV) effects in atoms andmolecules arise from $Z^0$ boson exchange between electrons and the nucleus,and from the magnetic interaction between electrons and the parity-violatingnuclear anapole moment. It has been proposed to study NSD-PV effects using anenhancement of the observable effect in diatomic molecules [D. DeMille$\textit{et al.}$, Phys. Rev. Lett. $\textbf{100}$, 023003 (2008)]. Here, wedemonstrate measurements of this type with sensitivity surpassing that of anyprevious atomic PV measurement, using the test system${^{138}\mathrm{Ba^{19}F}}$. We show that systematic errors associated with ourtechnique can be suppressed to at least the level of the present statisticalsensitivity. With $\sim\!170$ hours of data, we measure the matrix element,$W$, of the NSD-PV interaction with uncertainty $\delta W/(2\pi)<0.7$ Hz, foreach of two configurations where $W$ must have different signs. Thissensitivity would be sufficient to measure NSD-PV effects of the sizeanticipated across a wide range of nuclei.

Measuring Nuclear Spin Dependent Parity Violation With Molecules: Experimental Methods and Analysis of Systematic Errors