Molecular Lattice Clocks in the Optical Domain

Weakly bound molecules promise unparalleled sensitivity to temporal variations of the proton-to-electron mass ratio\footnote{Zelevinsky T, Kotochigova S, Ye J, Phys. Rev. Lett. 100 043201 (2008)} and in searches for new interactions beyond the Standard Model\footnote{Borkowski M, Buchachenko AA, Ciuryło R, Julienne PS, Yamada H, Kikuchi Y, Takasu Y, Takahashi Y 2018 Sci. Rep. 9, 14807 (2019)}. Both applications, however, rely on measurements of vibrational state positions of yet unrealized accuracy. To mitigate this, we propose to observe clock $^1$S$_0$-$^3$P$_0$ transitions in weakly bound bosonic $^{174}$Yb$_2$ molecules\footnote{Borkowski M, Phys. Rev. Lett. 120 083202 (2018)} facilitated by applying an external magnetic field\footnote{Taichenachev AV, et al. Phys. Rev. Lett. 96 083001 (2006)}. We predict the positions of molecular clock lines using photoassociation spectroscopy data for the ground state~\footnote{Borkowski M, Buchachenko AA, Ciuryło R, Julienne PS, Yamada H, Kikuchi Y, Takahashi K, Takasu Y, and Takahashi Y Phys. Rev. A 96 063405 (2017)}, and ab initio long range parameters\footnote{Porsev SG, Safronova MS, Derevianko A, and Clark CW Phys. Rev. A 89 012711 (2014)} and the recently measured $^{174}$Yb $^1$S$_0$-$^3$P$_0$ scattering length\footnote{Franchi L, et al. New J. Phys. 19 103037 (2017)} for clock state vibrational energies. The necessary ground state Yb$_2$ molecules could be efficiently produced by STIRAP. Thanks to favorable Franck-Condon factors the magnetically induced molecular Rabi frequencies can be comparable to the atomic Rabi frequencies under same laser intensities and magnetic fields. Using new ab initio potentials\footnote{P. Tecmer, et al., Int. J. Quant. Chem. 119, e25983 (2019) } we also evaluate the sensitivity of the excited clock states to changes in the proton-to-electron mass ratio.