Entanglement, nonclassical properties and geometric phase of Raman photon pairs in the presence of time-dependent coupling

In this paper, we develop the model of the 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 time-dependent coupling effect. We show that these quantifiers are very sensitive to the change of the Rabi frequency and time, exhibiting substantial phenomena that are depending on the kind of coupling between the atom and photons. Finally, we explore the relationship between the quantum quantifiers in terms of the physical parameters with and without time-dependent coupling effect.