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Accurate measurements of different transition frequencies between atomiclevels of the electronic and hyperfine structure over time are used toinvestigate temporal variations of the fine structure constant $\alpha$ and theproton-to-electron mass ratio $\mu$. We measure the frequency of the$^2S_{1/2}\rightarrow {^2F_{7/2}}$ electric octupole (E3) transition in$^{171}$Yb$^+$ against two caesium fountain clocks as $f(E3) =642\,121\,496\,772\,645.36(25)$~Hz with an improved fractional uncertainty of$3.9\times 10^{-16}$. This transition frequency shows a strong sensitivity tochanges of $\alpha$. Together with a number of previous and recent measurementsof the $^2S_{1/2}\rightarrow {^2D_{3/2}}$ electric quadrupole transition in$^{171}$Yb$^+$ and with data from other elements, a least-squares analysisyields $(1/\alpha)(d\alpha/dt)=-0.20(20)\times 10^{-16}/\mathrm{yr}$ and$(1/\mu)(d\mu/dt)=-0.5(1.6)\times 10^{-16}/\mathrm{yr}$, confirming a previouslimit on $d\alpha/dt$ and providing the most stringent limit on $d \mu/dt$ fromlaboratory experiments.

Improved limit on a temporal variation of $m_p/m_e$ from comparisons of Yb$^+$ and Cs atomic clocks