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

Abstract

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 ${\nu }_{E3}/{\nu }_{E2}=0.932829404530965376(32)$. 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 $1.0(1.1)\times 10^{-18}/\mathrm{yr}$ and of the proton-to-electron mass ratio $\mu$ to $-8(36)\times 10^{-18}/\mathrm{yr}$. Using the annual variation of the Sun's gravitational potential at Earth $\Phi$, 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 $(c^2/\mu )(d\mu /d\Phi )=7(45)\times 10^{-8}$.

6 pages, 3 figures

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