Comparisons of single-ion Yb$^+$ and Cs fountain clocks for searches for new physics*

We employ two single-ion Yb$^+$ optical clocks that use the $^2$S$_{1/2} \to {}^2$F$_{7/2}$ electric octupole (E3) transition as the reference. Because of their $3\times 10^{-18}$ uncertainty and the strong sensitivity of the transition frequency on the fine structure constant $\alpha$, comparisons with other atomic clocks enable improvements in searches for temporal variations of $\alpha$. A particularly suitable transition for such a comparison is the $^2$S$_{1/2} \to {}^2$D$_{3/2}$ electric quadrupole transition of the same ion, that we regularly use to test frequency shifts of the E3 transition induced by residual fields on a magnified scale. Besides investigations for variations of $\alpha$, long-term comparisons between the Yb$^+$ and Cs fountain clocks, with their frequency being sensitive to the proton-to-electron mass ratio $\mu$, allow us to improve present limits on the temporal variation of $\mu$ and use the data for searches for ultralight scalar dark matter.