Hyperfine rovibrational states of H$_3^+$ in a weak external magnetic field

TL;DR

This paper calculates the rovibrational and hyperfine energy levels of H₃⁺ in a weak magnetic field, providing a methodology for future spectroscopic studies of polyatomic molecules.

Contribution

It introduces a new computational approach to analyze hyperfine-Zeeman effects in polyatomic molecules like H₃⁺ under weak magnetic fields.

Findings

Computed rovibrational-hyperfine-Zeeman energy levels for H₃⁺

Developed a methodology applicable to higher-energy states and other molecules

Guides future quantum logic spectroscopy experiments

Abstract

Rovibrational energies, wave functions, and Raman transition moments are reported for the lowest-energy states of the H$_3^+$ molecular ion including the magnetic couplings of the proton spins and molecular rotation in the presence of a weak external magnetic field. The rovibrational-hyperfine-Zeeman Hamiltonian matrix is constructed and diagonalized using the rovibrational eigenstates and the proton spin functions. The developed methodology can be used to compute hyperfine-Zeeman effects also for higher-energy rovibrational excitations of H$_3^+$ and other polyatomic molecules. These developments will guide future experiments extending quantum logic spectroscopy to polyatomic systems.