Molecular parity nonconservation in nuclear spin couplings

The weak interaction does not conserve parity, which is apparent in many nuclear and atomic phenomena. However, thus far, parity nonconservation has not been observed in molecules. Here we consider nuclear-spin-dependent parity-nonconserving contributions to the molecular Hamiltonian. These contributions give rise to a parity-nonconserving indirect nuclear spin-spin coupling which can be distinguished from parity-conserving interactions in molecules of appropriate symmetry, including diatomic molecules. We estimate the magnitude of the coupling, taking into account relativistic corrections. Finally, we propose and simulate an experiment to detect the parity-nonconserving coupling using liquid- or gas-state zero-field nuclear magnetic resonance of electrically oriented molecules and show that ${}^1\mathrm{H}{}^{19}\mathrm{F}$ should give signals within the detection limits of current atomic vapor-cell magnetometers.

Figure 1

Experimental arrangement. (a) The apparatus includes a sample made of polar achiral molecules, each of which is a two-spin heteronuclear spin system oriented by an electric field $\mathit{E}$ produced by high-voltage (HV) electrodes. The nuclear spin state is prepared such that the initial magnetization is oriented along ${\mathit{M}}_0$, and magnetometers (depicted here as glass vapor cells) are used to measure the nuclear spin magnetization projection along ${\mathit{B}}_{\mathrm{Det}}$. (b) Nuclear spin eigenstates for various electric-field conditions. In the absence of any applied fields are three degenerate triplet states and a singlet state, separated by the $J$ coupling. Application of a dc electric field introduces a residual dipole-dipole coupling of strength $\overline{D}$ that shifts the $\left|T_0\right.〉$ state by $\overline{D}$ and the $\left|T_{\pm }\right.〉$ states by $-\overline{D}/2$. An ac electric field modulates the triplet states such that the average $\left|S_0\right.〉\leftrightarrow \left|T_0\right.〉$ separation is $J+\overline{D}/2$ and the average $\left|T_0\right.〉\leftrightarrow \left|T_{\pm }\right.〉$ separation is $3\overline{D}/4$.

Figure 2

Evolution of nuclear magnetization at zero magnetic field. Vector diagrams show the evolution of $\mathit{I}$ and $\mathit{S}$ magnetization, starting from $I_x-S_x$. Simulated signals along $\widehat{x}$ and $\widehat{y}$, assuming an initial state proportional to ${\gamma }_I{I}_x-{\gamma }_S{S}_x$. (a) Evolution under the isotropic $J$ coupling. (b) Including a static $\overline{J_z^{\left(1\right)}}$. (c) With a resonantly modulated $\overline{J_z^{\left(1\right)}}$. (d) Including the residual dipole-dipole coupling due to alignment by the electric field. In all cases, the spins evolve only in the $\widehat{x}\widehat{y}$ plane.

Figure 3

Electric-field phase cycling. Dependence of $B_x$ (parity-conserving) and $B_y$ (PNC) signals on the phase of the electric-field modulation.