  Applying the techniques of light-front quantization to quantize a scalar
field in a monochromatic gravitational wave background, we manage to
investigate the response of the Unruh-DeWitt detector coupled to a scalar field
in the presence of a gravitational wave for the two cases moving along a
free-falling trajectory and a constant-accelerating trajectory. The transition
rate of the Unruh-DeWitt detector, in both cases, is different from the result
with no gravitational wave, and the leading-order correction due to the
gravitational wave survives the long-wavelength limit that formally takes the
wavelength of the gravitational wave to infinity. This new effect of the
gravitational wave on a quantum system is qualitatively different from that on
a classical mechanical system, and cannot be understood in terms of
gravitational wave tidal force.
