  We firstly generalize the massive scalar propagator for planar gravitational
waves propagating on Minkowski space obtained recently in Ref. [1]. We then use
this propagator to study the response of a freely falling Unruh-DeWitt detector
to a gravitational wave background. We find that a freely falling detector
completely cancels the effect of the deformation of the invariant distance
induced by the gravitational waves, such that the only effect comes from an
increased average size of scalar field vacuum fluctuations, the origin of which
can be traced back to the change of the surface in which the gravitational
waves fluctuate. The effect originates from the quantum interference between
propagation on off-shell detector's trajectories which probe different spatial
gravitational potential induced by the gravitational backreaction from
gravitational waves, and it is therefore purely quantum. When resummed over
classical graviton insertions, gravitational waves generate cuts on the
imaginary axis of the complex $\Delta \tau$-plane (where $\Delta \tau =
\tau-\tau'$ denotes the difference of proper times), and the discontinuity
across these cuts is responsible for a continuum of energy transitions induced
in the Unruh-DeWitt detector. Not surprisingly, we find that the detector's
transition rate is exponentially suppressed with increasing energy and the mass
of the scalar field. What is surprising, however, is that the transition rate
is a non-analytic function of the gravitational field strain. This means that,
no matter how small is the gravitational field amplitude, expanding in powers
of the gravitational field strain cannot approximate well the detector's
transition rate.
