Quantum interactions between a laser interferometer and gravitational waves

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.