  We study the interaction between gravitational waves and a quantum two-level
system consisting of a spin 1/2 particle using the formalism of the proper
detector frame. This approach highlights the effects of gravitational waves on
both the particles and the observer, emphasizing that only relative
measurements can be made. Specifically, within this framework, the
gravitational field of the waves is described using the gravitoelectromagnetic
analogy. The interaction of the system is then determined by the
gravitomagnetic field of the wave, which induces a time-dependent perturbation.
We analyze this perturbation for both generic frequencies and resonance
conditions, and discuss its implications.
