Probing Fundamental Symmetries of Deformed Nuclei in Symmetric Top Molecules

Precision measurements of Schiff moments in heavy, deformed nuclei are sensitive probes of beyond standard model $T$, $P$ violation in the hadronic sector. While the most stringent limits on Schiff moments to date are set with diamagnetic atoms, polar polyatomic molecules can offer higher sensitivities with unique experimental advantages. In particular, symmetric top molecular ions possess $K$ doublets of opposite parity with especially small splittings, leading to full polarization at low fields, internal comagnetometer states useful for rejection of systematic effects, and the ability to perform sensitive searches for $T$, $P$ violation using a small number of trapped ions containing heavy exotic nuclei. We consider the symmetric top cation ${}^{225}\mathrm{Ra}{\mathrm{OCH}}_3^{+}$ as a prototypical and candidate platform for performing sensitive nuclear Schiff measurements and characterize in detail its internal structure using relativistic ab initio methods. The combination of enhancements from a deformed nucleus, large polarizability, and unique molecular structure make this molecule a promising platform to search for fundamental symmetry violation even with a single trapped ion.

Figure 1

Labeled ${}^{225}\mathrm{Ra}{\mathrm{OCH}}_3^{+}$ STMs in stretched states, grouped by energy and total angular momentum projection $m_F$. The internuclear axis runs from the negatively charged end (methyl group) to the positively charged metal (radium). $K$ is the molecule-frame projection of angular momentum without spin $N$, while $m_N$ is its projection onto the lab frame. Nuclear spins for each spin-$1/2$ nucleus (${}^1\mathrm{H}$, ${}^{225}\mathrm{Ra}$) are indicated. The $|K|=1$ states correspond to the mixed para nuclear spin isomer (NSI) of the hydrogens, while the $K=0$ state coincides with the stretched ortho NSI.

Figure 2

Lab frame dipole moment of hyperfine states of the $|N=1,|K|=1⟩$ manifold in the limit where the $K$ doublets are fully mixed yet rotational mixing is negligible. High, low, and no field seekers correspond to states with negative, positive, and zero dipole moment ($K\times m_N=+1$, 0, and $-1$). The jumps indicate avoided crossings.

Figure 3

Level structure and Schiff moment sensitivities for the 24 hyperfine states of the $N=|K|=1$ manifold in the decoupled regime ($1\mathrm{V}/\mathrm{cm}$), grouped by $m_F$ and their Stark manifold ($K\times m_N$). Gold states have $+1/4$ effective Schiff sensitivity, while blue states have $-1/4$ effective Schiff sensitivity. Dashed lines denote zero Schiff sensitivity. Labels above or below the states indicate the effective $g$ factor at zero magnetic field, in terms of nuclear magnetons (${\mu }_N$). Table S4 in Ref. [61] lists the admixtures for each state.