Laser-coolable ${\mathrm{AcOH}}^{+}$ ion for $\mathcal{CP}$-violation searches

The ${\mathrm{AcOH}}^{+}$ molecular ion is identified as a prospective system to search for $\mathcal{CP}$-violation effects. According to our study ${\mathrm{AcOH}}^{+}$ belongs to the class of laser-coolable polyatomic molecular cations implying a large coherence time in the experiments to study symmetry-violating effects of fundamental interactions. We perform both nuclear and high-level relativistic coupled cluster electronic structure calculations to express the experimentally measurable $\mathcal{T},\mathcal{P}$-violating energy shift in terms of fundamental quantities such as the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment ($e\mathrm{EDM}$) and dimensionless scalar-pseudoscalar nuclear-electron interaction constant. We further express nuclear MQM in terms of the strength constants of $\mathcal{CP}$-violating nuclear forces: quantum chromodynamics vacuum angle $\overline{\theta }$ and quark chromo-EDMs. The equilibrium structure of ${\mathrm{AcOH}}^{+}$ in the ground and the four lowest excited electronic states was found to be linear. The calculated Franck-Condon factors and transition dipole moments indicate that the laser cooling using an optical cycle involving the first excited state is possible for the trapped ${\mathrm{AcOH}}^{+}$ ions with the Doppler limit estimated to be $\sim$4 nK. The lifetime of the ($0,1^1,0$) excited vibrational state considered as a working one for MQM and $e\mathrm{EDM}$ search experiments is estimated to be $\sim 0.4$ s.

Figure 1

Potential energies of the ground (1)1/2 and excited states of the ${\mathrm{AcOH}}^{+}$ ion as functions of ${\mathrm{R}}_{\text{Ac-O}}$ (left), ${\mathrm{R}}_{\text{O-H}}$ (center), and the valence Ac-O-H angle (right) with other parameters fixed at the equilibrium values for the ground state. Energies are given with respect to the ground-state equilibrium point.

Figure 2

Isosurfaces and cross-section view of squared absolute values of approximate natural transition spinors (NTSs) for the (1)1/2 $\to$ (1)3/2 transition in ${\mathrm{AcOH}}^{+}$.

Figure 3

The absolute value of the (1)1/2-(1)3/2 transition dipole moment as a function of ${\mathrm{R}}_{\text{Ac-O}}$, calculated at the FS-RCCSD level. Other parameters are fixed at the equilibrium values for the ground state (${\mathrm{R}}_{\text{O-H}}=0.960$ Å, $\angle$(Ac-O-H) $={180}^{\circ }$).