LIGO's detection of gravitational waves marks a first step in measurable
effects of general relativity on quantum matter. In its current operation,
laser interferometer gravitational-wave detectors are already quantum limited
at high frequencies, and planned upgrades aim to decrease the noise floor to
the quantum level over a wider bandwidth. This raises the interesting idea of
what a gravitational-wave detector, or an optomechanical system more generally,
may reveal about gravity beyond detecting gravitational waves from highly
energetic astrophysical events, such as its quantum versus classical nature. In
this paper we develop a quantum treatment of gravitational waves and its
interactions with the detector. We show that the treatment recovers known
equations of motion in the classical limit for gravity, and we apply our
formulation to study the system dynamics, with a particular focus on the
implications of gravity quantization. Our framework can also be extended to
study alternate theories of gravity and the ways in which their features
manifest themselves in a quantum optomechanical system
