Scalar-Mediated Quantum Forces Between Macroscopic Bodies and Interferometry

We study the quantum force between classical objects mediated by massive scalar fields bilinearly coupled to matter. The existence of such fields is motivated by dark matter, dark energy, and by the possibility of a hidden sector beyond the Standard Model. We introduce the quantum work felt by an arbitrary (either rigid or deformable) classical body in the presence of the scalar and show that it is finite upon requiring conservation of matter. As an example, we explicitly show that the quantum pressure inside a Dirichlet sphere is finite -- up to renormalizable divergences. Inside the bodies the scalar acquires an effective mass, leading to a behaviour for the quantum force which, in the case of rigid bodies, is reminiscent of the transition between the Casimir and Casimir-Polder forces. With this method we compute the scalar-induced quantum force in simple planar geometries. In plane-point geometry we show how to compute the contribution of the quantum force to the phase shift observable in atom interferometers. We show that atom interferometry is likely to become a competitive search method for light particles bilinearly coupled to matter, provided that the interferometer arms have lengths below ~10 cm.