Proposal for an optical interferometric measurement of the gravitational red-shift with satellite systems

The Einstein Equivalence Principle (EEP) underpins all metric theories of gravity. One of its key aspects is the local position invariance (LPI) of non-gravitational experiments, which is captured by the gravitational red-shift. The iconic gravitational red-shift experiment places two fermionic systems, used as clocks, in different gravitational potentials and compares them using the electromagnetic field. However, the electromagnetic field itself can be used as a clock, by comparing the phases acquired by two optical pulses propagating through different gravitational potentials. A fundamental point in the implementation of a satellite large-distance optical interferometric experiment is the suppression of the first-order Doppler effect, which dominates the weak gravitational signal necessary to test the EEP. Here, we propose a novel scheme to suppress it, by subtracting the phase-shifts measured in the one-way and in the two-way configuration between a ground station and a satellite. We present a detailed analysis of this technique within the post-Newtonian framework and perform some simulations of its performance using realistic satellite orbits and the state-of-the-art fiber technology at the telecom wavelength of 1550 nm.