Spin gravitational resonance and graviton detection

We develop a gravitational analogue of spin magnetic resonance, called spin gravitational resonance, whereby a gravitational wave interacts with a magnetic field to produce a spin transition. In particular, an external magnetic field separates the energy spin states of a spin-$1/2$ particle, and the presence of the gravitational wave produces a perturbation in the components of the magnetic field orthogonal to the gravitational-wave propagation. In this framework we test Dyson’s conjecture that individual gravitons cannot be detected. Although we find no fundamental laws preventing single gravitons being detected with spin gravitational resonance, we show that it cannot be used in practice, in support of Dyson’s conjecture.

Figure 1

A constant external magnetic field $\mathbf{B}$ (depicted here lying in the $x\text{−}z$ plane) lifts the degeneracy of spin states. In the ground state, the particle’s spin (red arrow) is aligned with the magnetic field. When the propagation direction of the plane GW is not (anti-)parallel to the magnetic field, the interaction of the magnetic field with the GW in the plane perpendicular to its propagation produces the perturbation that results in the transition between spin states.