Highly Sensitive Molecular Ion Probe for Variation of the Proton-to- Electron Mass Ratio

Rovibrational transitions in molecules provide an unambiguous connection to the proton-to-electron mass ratio ($\mu$). However, difficulties in molecular state preparation, detection and control over systematics have prevented setting new limits on $\mu$-variation at the level set by analogous measurements in atoms. We identify a new molecular ion, TeH$^+$, which has unique properties that mitigate these challenges. Its electronic structure leads to highly diagonal Franck-Condon factors, which can be exploited to implement fast optical state preparation. Combined with its deep ground state potential well in the optical domain, statistical averaging for a single TeH$^+$ ion leads to a fractional precision comparable to that of single ion atomic clocks. Its 0$^+$ ground state is also relatively insensitive to systematic Zeeman and Stark shifts. These features all together reveal a promising candidate for setting a new limit on $\mu$-variation.