  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.
