Abstract
In this paper, we develop a model for four-level double Raman pairs by exploiting the required optimal conditions for this system that are feasible with real experimental realization. We investigate qualitatively the entanglement, statistical properties, and geometric phase for the pair of Stokes and anti-Stokes photons in the presence of the relativistic motion. We show that these quantifiers are very sensitive to the change of the Rabi frequency under relativistic motion, exhibiting substantial phenomena that depend on this kind of the coupling between the atom and photons. Finally, we explore the relationship between the quantum quantifiers for constant and time-dependent coupling.