Testing the nonclassicality of gravity with the field of a single delocalized mass

Most of the existing proposals for laboratory tests of a quantum nature of gravity are based on the use of two delocalized masses or harmonically bound masses prepared in pure quantum states with large enough spatial extent. Here a setup is proposed that is based on a single delocalized mass coupled to a harmonically trapped test mass (undergoing first expansion and then compression) that moves under the action of gravity. We investigate the in-principle feasibility of such an experiment, which turns out to crucially depend on the ability to tame Casimir-Polder forces. We thus proceed with a design aimed at achieving this, trying at the same time to take advantage of these forces rather than only fighting them.