Analysis of Sun/Moon gravitational redshift tests with the STE-QUEST space mission

The Space-Time Explorer and Quantum Equivalence principle Space Test (STE-QUEST) space mission will perform tests of the gravitational redshift in the field of the Sun and the Moon to high precision by frequency comparisons of clocks attached to the ground and separated by intercontinental distances. In the absence of Einstein equivalence principle (EP) violation, the redshift is zero up to small tidal corrections, as the Earth is freely falling in the field of the Sun and Moon. Such tests are thus null tests, allowing us to bound possible violations of the EP. Here we analyze the Sun/Moon redshift tests using a generic EP-violating theoretical framework, with clocks minimally modelled as two-level atoms. We present a complete derivation of the redshift (including both general relativity (GR) and non-GR terms) in a realistic experiment such as the one envisaged for STE-QUEST. We point out and correct an error in previous formalisms linked to the atom's recoil not being properly taken into account.