Quantum two-level systems and gravitational waves

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.