  We investigate, in the framework of linearized quantum gravity, the induced
quantum gravitational interaction between two ground-state objects with
permanent quadrupole moments, which are subjected to an external gravitational
radiation field. Compared with the nonpolar case, there exists an additional
term in the leading-order field-induced interobject interaction between two
polar objects. This term arises when a real graviton is scattered by the same
object center with coupling between the two objects occurring via the exchange
of a single virtual graviton, and the interaction is thus relevant to the
number density of gravitons, the frequency and polarization of the external
gravitational field, as well as the permanent quadrupoles of the objects. Due
to the existence of such an additional term, the field-induced quantum
gravitational interaction between two polar objects can be significantly
different from that between nonpolar ones when the interobject distance is much
smaller than the wavelength of the external gravitational radiation field.
Although we model the external gravitational radiation as a quantized
monochromatic gravitational wave with a certain wave vector and polarization
for simplicity, it is possible to generalize to more realistic situations, such
as the case of a stochastic background of gravitational radiation.
