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Divalent atoms and ions with a singlet $S$ ground state and triplet $P$excited state form the basis of many high-precision optical atomic clocks.Along with the metastable $^{3}\mathrm{P}_{0}$ clock state, these atomicsystems also have a nearby metastable $^{3}\mathrm{P}_{2}$ state. Weinvestigate the properties of the electric quadrupole$^{1}\mathrm{S}_0$$\leftrightarrow$$^{3}\mathrm{P}_{2}$ transition with a focuson enhancing already existing optical atomic clocks. In particular, weinvestigate the $^{1}\mathrm{S}_0$$\leftrightarrow$$^{3}\mathrm{P}_{2}$transition in $^{27}\mathrm{Al}^{+}$ and calculate the differentialpolarizability, hyperfine effects, and other relevant atomic properties. Wealso discuss potential applications of this transition, notably that itprovides two transitions with different sensitivities to systematic effects inthe same species. In addition, we describe how the$^{1}\mathrm{S}_0$$\leftrightarrow$$^{3}\mathrm{P}_{2}$ transition can be usedto search for physics beyond the Standard Model and motivate investigation ofthis transition in other existing optical atomic clocks.

Enhancing Divalent Optical Atomic Clocks with the $^{1}\mathrm{S}_0$$\leftrightarrow$$^{3}\mathrm{P}_{2}$ Transition