Coherently Driven Number of Degenerate Three-Level Atoms with Parametric Amplifier

Figure 1

Schematic representation of a degenerate three-level laser with a degenerate parametric amplifier (DPA) and coupled to a two-mode vacuum reservoir. Here, , considered to be real and constant, is proportional to the amplitude of the pump mode that drives the nonlinear crystal (NLC), and is the amplitude of the driving coherent light that couples the top and bottom levels of the atom. And also is the cavity damping constant, and it is assumed the same for both transitions. The top, middle, and bottom levels of the three-level atom are denoted by , , and , respectively, where as are the number of atoms inside the cavity. When the atom makes a transition from level and from levels two photons with the same frequencies, , are emitted.