Accuracy estimations of overtone vibrational transition frequencies of optically trapped174Yb6Li molecules

Abstract

The attainable accuracy of the $X\phantom{\rule{0.16em}{0ex}}{}^{2}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Sigma}(v,N)=(0,0)\ensuremath{\rightarrow}({v}_{u},0)$ transition frequencies of optically trapped ${}^{174}$Yb${}^{6}$Li molecules are analyzed $({v}_{u}=1,2,3,4)$ to test the variation in the proton-to-electron mass ratio. We eliminate the Stark shifts induced by the trap and Raman lasers by choosing appropriate frequencies (magic frequencies). For ${v}_{u}=1$ and 2, we obtain more than one experimentally useful magic frequency, thereby leading to more choice in the trap laser. For ${v}_{u}=3$ and 4, the choice in the trap laser is limited. The systematic frequency uncertainty is given by the trap laser frequency detuning from the magic frequency and the fluctuation of the power ratio of the two Raman lasers and can be lower than 10${}^{\ensuremath{-}16}$ for all these transition frequencies. To obtain lower statistical uncertainty, measurement with ${v}_{u}=4$ is more advantageous than that with ${v}_{u}=1\ensuremath{-}3$.