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$_{3/2}(F=2)$ electric quadrupole (E2) and the $^2$S$_{1/2}(F=0)\to {}^2$F$_{7/2}(F=3)$ electric octupole (E3) transition of $^{171}$Yb$^{+}$ and measure the frequency ratio $ν_{\mathrm{E3}}/ν_{\mathrm{E2}}=0.932\,829\,404\,530\,965\,376(32)$. We determine the transition frequency $ν_{E3}=642\,121\,496\,772\,645.10(8)$ 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 $α$ to $1.0(1.1)\times10^{-18}/\mathrm{yr}$ and of the proton-to-electron mass ratio $μ$ to $-8(36)\times10^{-18}/\mathrm{yr}$. Using the annual variation of the Sun's gravitational potential at Earth $Φ$, we improve limits for a potential coupling of both constants to gravity, $(c^2/α) (dα/dΦ)=14(11)\times 10^{-9}$ and $(c^2/μ) (dμ/dΦ)=7(45)\times 10^{-8}$.

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