Open quantum system approach to the gravitational decoherence of spin-1/2 particles

This paper investigates the decoherence effect resulting from the interaction of squeezed gravitational waves with a system of massive particles in spatial superposition. We take into account two systems, one made up of spin-1/2 particles and the other of spinless particles, and use the quantum Boltzmann equation to study their decoherence. For the spin-1/2 particle system, our analysis reveals that the rate of decoherence depends on both the squeezing strength and the squeezing angle of the gravitational waves. Our results demonstrate that squeezed gravitational waves with squeezing strengths of $r_p\geq1.2$ and a squeezing angle of $\varphi_p=\pi/2$ can induce a 1 % decoherence within 1 s free falling of a cloud of spin-1/2 particles. In contrast, for the spinless particle system, the decoherence rate is weaker and depends solely on the squeezing strength of the gravitational waves and does not depend on the squeezing angle. As a consequence, in this case, the same amount of decoherence of the spin-1/2 particles can be reached when the system is two orders of magnitude more massive, the experiment ten times longer, and for squeezing strength $r_p\geq2.1$. This investigation sheds light on the relationship between squeezed gravitational waves and the coherence of spatial superposition states in systems of massive particles and their spin. The dependence of decoherence on squeezing strength and, in the case of spin-1/2 particles, on the squeezing angle paves the way for further exploration and understanding of the quantum-gravity connection. We suggest that such an experimental setup could also be employed to eventually investigate the level of squeezing effect (and hence quantum-related properties) of gravitational waves produced in the Early Universe from inflation.Comment: 40 pages, 8 figure