Tests of local position invariance using continuously running atomic clocks

Tests of local position invariance (LPI) made by comparing the relative redshift of atomic clocks based on different atoms have been carried out for a variety of pairs of atomic species. In most cases, several absolute frequency measurements per year are used to look for an annual signal, resulting in tests that can span on order of a decade. By using the output of continuously running clocks, we carry out LPI tests with comparable or higher precision after less than 1.5 years. These include new measurements of the difference in redshift anomalies β for hyperfine transitions in ⁸⁷Rb and ¹³³Cs and in ¹H and ¹³³Cs and a measurement comparing ⁸⁷Rb and ¹H, resulting in a stringent limit on LPI, βRb-βH=(-2.7±4.9)×10^-7. The method of making these measurements for continuous clocks is discussed.