Testing the Wave-Particle Duality of Gravitational Wave Using the Spin-Orbital-Hall Effect of Structured Light

Abstract

Probing the polarization of gravitational waves (GWs) would provide evidence of graviton, indicating the quantization of gravity. Motivated by the next generation of gravitational wave detectors, we make an attempt to study the possible helicity coupling of structured lights to GWs. With the analog between gravitational fields and the generic electromagnetic media, we present a 4-vector optical Dirac equation based on the Maxwell theory under the paraxial approximation. It is found that twisted lights propagating in a gravitational field can be viewed as a non-Hermitian system with PT symmetry. We further demonstrate that the coupling effect between angular momentums of the GWs and twisted lights may make photons undergo both dipole and quadrupole transitions between different orbital-angular-momentum (OAM) eigenstates and lead to some measurable optical features, including the central intensity brightening and macroscopic rotation of the intensity pattern for twisted lights. The former is spin-independent, while the latter is a spin-dependent phenomenon, both of which can be viewed alternatively as the spin-orbital-Hall effect of structured lights in the GWs and can serve as an indicator of the particle nature of GWs.