Detectability of post-Newtonian classical and quantum gravity via quantum clock interferometry

Understanding physical phenomena at the intersection of quantum mechanics and general relativity remains a major challenge in modern physics. While various experimental approaches have been proposed to probe quantum systems in curved spacetime, most focus on the Newtonian regime, leaving post-Newtonian effects such as frame dragging largely unexplored. In this study, we propose and theoretically analyze an experimental scheme to investigate how post-Newtonian gravity affects quantum systems. We consider two setups: (i) a quantum clock interferometry setup designed to detect the gravitational field of a rotating mass, and (ii) a scheme exploring whether such effects could be used to generate gravity-induced entanglement. Due to the symmetry of the configuration, the proposed setup is insensitive to Newtonian gravitational contributions but remains sensitive to the frame-dragging effect. Furthermore, our scheme allows for testing whether the observed gravity-induced entanglement is consistent with the quantum equivalence principle. While the predicted effects appear too small to detect with current technology, our scheme offers a starting point for future experiments probing post-Newtonian quantum gravitational effects.