Improved Limits for Violations of Local Position Invariance from Atomic Clock Comparisons

We compare two optical clocks based on the S-2(1/2)(F = 0) -> D-2(3/2) (F = 2) electric quadrupole (E2) and the S-2(1/2)(F = 0) -> F-2(7/2)(F = 3) electric octupole (E3) transition of Yb-171+ and measure the frequency ratio nu(E3)/nu(E2) = 0.932829404530965376(32), improving upon previous measurements by an order of magnitude. Using two caesium fountain clocks, we find nu(E3) = 642121496772645.10(8) Hz, the most accurate determination of an optical transition frequency to date. 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) x 10(-18)/yr and of the proton-to-electron mass ratio mu to -8(36) x 10(-18)/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) x 10(-9) and (c(2)/mu)(d mu/d Phi) = 7(45) x 10(-8).