Relativistic Effects in Atom and Neutron Interferometry and the   Differences Between Them
  In recent years there has been an enormous progress in matter wave interferometry. The Colella- Overhauser-Werner (COW) type of neutron interferometer and the Kasevich-Chu (K-C) atom interferometer, are the prototype of such devices and the issue of whether they are sensitive to relativistic effects has recently aroused much controversy. We examine the question of to what extent the gravitational red shift, and the related twin paradox effect can be seen in both of these atom and neutron interferometers. We point out an asymmetry between the two types of devices. Because of this, the non-vanishing, non-relativistic residue of both effects can be seen in the neutron interferometer, while in the K-C interferometer the effects cancel out, leaving no residue, although they could be present in other types of atom interferometers. Also, the necessary shifting of the laser frequency (chirping) in the atom interferometer effectively changes the laboratory into a free-fall system, which could be exploited for other experiments. 
Daniel M. Greenberger, Wolfgang P. Schleich, and Ernst M. Rasel
quant-ph physics.atom-ph