Prospects for Polar Molecular Ion Optical Probe of Varying Proton-Electron Mass Ratio

TL;DR

This paper explores the potential of using polar molecular ions, specifically TeH$^+$, as optical probes for detecting variations in the proton-electron mass ratio, highlighting their suitability due to favorable vibrational properties and low polarizability.

Contribution

It demonstrates that polar molecules like TeH$^+$ can be effectively used for precision measurements of fundamental constants, overcoming previous concerns about their polarizability effects.

Findings

Single-photon spectroscopy on TeH$^+$ is feasible with high precision.

Low polarizability in certain rotational states reduces Stark shifts.

Projected sensitivity could detect variations in the proton-electron mass ratio at 10^{-18} per year.

Abstract

Molecules with deep vibrational potential wells provide optical intervals sensitive to variation in the proton-electron mass ratio ($\mu$). On one hand, polar molecules are of interest since optical state preparation techniques have been demonstrated for such species. On the other hand, it might be assumed that polar species are unfavorable candidates, because typical molecule-frame dipole moments reduce vibrational state lifetimes and cause large polarizabilities and associated Stark shifts. Here, we consider single-photon spectroscopy on a vibrational overtone transition of the polar species TeH$^+$, which is of practical interest because its diagonal Franck-Condon factors should allow rapid state preparation by optical pumping. We point out that all but the ground rotational state obtains a vanishing low-frequency scalar polarizability from coupling with adjacent rotational states, because of a fortuitous relationship between rigid rotor spacings and dipole matrix elements. We project that for good choices of spectroscopy states, demonstrated levels of field control should make possible uncertainties of order $1 \times 10^{-18}$, similar to those of leading atomic ion clocks. The moderately long lived vibrational states of TeH$^+$ make possible a frequency uncertainty approaching $1 \times 10^{-17}$ with one day of averaging for a single trapped ion. Observation over one year could probe for variation of $\mu$ with a sensitivity approaching the $1 \times 10^{-18}/\textrm{yr}$ level.