  We consider tests of short-distance modifications of gravity based on neutron
interferometry in the scenario of large extra dimensions. Avoiding the
non-computability problem in the calculation of the internal gravitational
potential of extended sources, typical of models with zero-width brane, we
determine the neutron optical potential associated with the higher-dimension
gravitational interaction between the incident neutron and a material medium in
the context of thick brane theories. Proceeding this way, we identify the
physical quantity of the extra dimension model that the neutron interferometry
is capable of constraining. We also consider interferometric experiments in
which the phase shifter is an electric field, as in the test of the
Aharanov-Casher effect. We argue that this experiment, with this non-baryonic
source, can be viewed as a test of the short-range behavior of Post-Newtonian
parameters that measure the capacity of the pressure and the internal energy
for producing gravity.
