New Test of Weak Equivalence Principle Using Frequency Comparisons of high-precision Clocks

The Einstein Equivalence Principle plays a central role in understanding gravity and spacetime. In its weak form, weak equivalence principle (WEP), it implies the universality of free fall. Beyond the Newton frame, we investigate the changes of clock rates in the presence of WEP violation described by E$\ddot{\text{o}}$tv$\ddot{\text{o}}$s parameter $\delta$. Then, we propose a novel test of WEP using frequency measurements from the comparisons of high-precision clocks. In the proposed test, the frequency comparisons of clocks comoving with the freely falling frame contain the gravity in gravitational redshift and dynamical acceleration in the second-order Doppler effect, which makes such a test possible. In contrast to traditional tests, measuring the difference on E$\ddot{\text{o}}$tv$\ddot{\text{o}}$s parameter between two materials of different compositions, our proposal allows for measuring the E$\ddot{\text{o}}$tv$\ddot{\text{o}}$s parameter for single "test" body. This is a new window on testing WEP. By searching for a daily variation of frequency difference between strontium optical clocks linked by optical links, about Earth for instance, we obtain the upper limit of E$\ddot{\text{o}}$tv$\ddot{\text{o}}$s parameter as such $\delta_{\text{E}}=(0.3\pm0.9)\times10^{-4}$.