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

We compare two optical clocks based on the ^2_{1/2}(F=0)\to {}^2_{3/2}(F=2)electric quadrupole (E2) and the ^2_{1/2}(F=0)\to {}^2_{7/2}(F=3)electric octupole (E3) transition of ^{171}b^{+}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...