Wave-particle duality of gravitational radiation

We study the continuous quantum measurement of gravitational radiation. This is typically done by coupling the radiation to a meter, such as a resonant mass detector or an interferometer, which is subsequently read out by a detector. We find that the detector employed determines whether the gravitational field exhibits wave or particle characteristics. A linear detector, such as a homodyne detector, yields no signal for a field in a Fock state and a signal proportional to the amplitude of a field in a coherent state. Such a linear detector thus supports a wave-like interpretation. By contrast, the signal from a detector coupled to the meter's energy is non-zero only when the incident radiation contains at least a single graviton, resulting in a quantum jump in energy equal to the energy of the absorbed graviton. Our results extend the principle of complementarity to quantized gravitational radiation, demonstrating the detector dependence of the graviton, and indicates that conceptually simple modifications to gravitational-wave detectors can make them graviton counters.