Improved limits for violations of local position invariance from atomic clock comparisons

We compare two optical clocks based on the ${}^2$S${1/2}(F=0)\to {}^2$D${3/2}(F=2)$electricquadrupole(E2)andthe$^2$S${1/2}(F=0)\to {}^2$F${7/2}(F=3)$electricoctupole(E3)transitionof$^{171}$Yb$^{+}$ and measure the frequency ratio ${\nu }_{\mathrm{E}3}\mathrm{/}{\nu }_{\mathrm{E}2}=0.932829404530965376(32)$. We determine the transition frequency ${\nu }_{E3}=642121496772645.10(8)$ Hz using two caesium fountain clocks. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant $\alpha$ to $1.0(1.1)\times {10}^{-18}\mathrm{/}\mathrm{y}\mathrm{r}$ and of the proton-to-electron mass ratio $\mu$ to $-8(36)\times {10}^{-18}\mathrm{/}\mathrm{y}\mathrm{r}$. Using the annual variation of the Sun’s gravitational potential at Earth $\mathrm{\Phi }$, we improve limits for a potential coupling of both constants to gravity, $(c^2/\alpha) (d\alpha/d\Phi)=14(11)\times 10^{-9}$and$(c^2/\mu) (d\mu/d\Phi)=7(45)\times 10^{-8}$.