Optical Response of a Position-Dependent Optomechanical System With N-Type Four-Level Atoms

Cavity optomechanics explores the interaction between light and mechanical systems through radiation pressure. This interdisciplinary field merges principles from quantum mechanics and quantum optics provides powerful tools for generating and controlling quantum states. In this research, we theoretically investigated a four-level N-atomic system within the context of optomechanics. The oscillating mirror possesses a mass that varies with position and exhibits a singularity. We analyzed the dynamics using Heisenberg–Langevin equations and calculated steady-state solutions, studied optical response through both analytical and numerical methods. The main focus of this study was optical response within the domain of position-dependent effective mass. Our findings revealed that the output field representing transmission exhibits variations and shift with $\alpha$, the nonlinear parameter of the position dependent effective mass. These variations not only impact transmission but also alter the dispersion and phase of the output field.