Canceling spin-dependent contributions and systematic shifts in precision spectroscopy of the molecular hydrogen ions

Abstract

We consider the application of a basic principle of quantum theory, the tracelessness of a certain class of hamiltonians, to the precision spectroscopy of the molecular hydrogen ions. We show that it is possible to obtain the spin-averaged transition frequencies between states from a simple weighted sum of experimentally accessible spin-dependent transition frequencies. We discuss the cases ${\mathrm{H}}_2^{+}$ and ${\mathrm{HD}}^{+}$, which are distinct in the multipole character of their rovibrational transitions. Inclusion of additional frequencies permits canceling also the electric quadrupole shift, the Zeeman shift and partially the Stark shift. In this context, we find that measuring electric quadrupole transitions in ${\mathrm{HD}}^{+}$ is advantageous. The required experimental effort appears reasonable.

References in corpus (7)

• Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD+
• Fundamental transitions and ionization energies of the hydrogen molecular ions at the few ppt level
• Rotational spectroscopy of cold, trapped molecular ions in the Lamb-Dicke regime
• The static and dynamic polarisability, and the Stark and black-body radiation frequency shifts of the molecular hydrogen ions H2+, HD+, and D2+
• Test of the theoretical hyperfine structure of the molecular hydrogen ion at the 1-ppm level
• Vibrational spectroscopy of H2+: hyperfine structure of two-photon transitions
• Laser-stimulated electric quadrupole transitions in the molecular hydrogen ion H2+

Cited by in corpus (4)

• Prospects for Polar Molecular Ion Optical Probe of Varying Proton-Electron Mass Ratio
• Prospects for the determination of fundamental constants with beyond-state-of-the-art uncertainty using molecular hydrogen ion spectroscopy
• Production of HD Molecules in Definite Hyperfine Substates
• Hyperfine structure and electric quadrupole transitions in the deuterium molecular ion