  Atomic interference experiments can probe the gravitational redshift via the
internal energy splitting of atoms and thus give direct access to test the
universality of the coupling between matter-energy and gravity at different
spacetime points. By including possible violations of the equivalence principle
in a fully quantized treatment of all degrees of freedom, we characterize how
the sensitivity to gravitational redshift violations arises in atomic clocks
and atom interferometers, as well as their underlying limitations.
Specifically, we show that: (i.) Contributions beyond linear order to trapping
potentials lead to such a sensitivity of trapped atomic clocks. (ii.) While
Bragg-type interferometers, even with a superposition of internal states, with
state-independent, linear interaction potentials are at first insensitive to
gravitational redshift tests, modified configurations, for example by
relaunching the atoms, can mimic such tests tests under certain conditions.
(iii.) Guided atom interferometers are comparable to atomic clocks. (iv.)
Internal transitions lead to state-dependent interaction potentials through
which light-pulse atom interferometers can become sensitive to gravitational
redshift violations.
