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

Understand

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 $\nu_{\mathrm{E3}}/\nu_{\mathrm{E2}}=0.932\,829\,404\,530\,965\,376(32)$.

• We determine the transition frequency $\nu_{E3}=642\,121\,496\,772\,645.10(8)$ 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 $\alpha$ to $1.0(1.1)\times10^{-18}/\mathrm{yr}$ and of the proton-to-electron mass ratio $\mu$ to $-8(36)\times10^{-18}/\mathrm{yr}$.