Optomechanical electromagnetically induced transparency in inverted atomic configurations: a comparative view

We study electromagnetically induced transparency (EIT), which is affected by cavity optomechanics in different atomic configurations (V and $\Lambda$). The cavity mode is depicted as a probe field, and a classical driving field is applied to the atomic medium as the control laser in each system. Interaction between the cavity mode, atomic media and the oscillating mirror of the cavity can change the susceptibility of the atomic ensemble. Equations of motion demonstrate a system of nonlinear equations for each system. Nonlinearity of equations is a result of interaction between the cavity mode and atomic transitions. The equations are solved via a perturbation method. The results show two different aspects of atom-assisted optomechanics in V-type system: a common transparency window and an amplifying process in a transparency window that does not occur in the $\Lambda$ configuration, notable as a considerable difference between the proposed systems. It is shown that classical field detuning leads to different changes in the susceptibility of both systems; other values of cavity detuning, except in the resonant case, can guarantee the occurrence of EIT in the system. For the initial value of the cavity field, a negative region appears in absorption spectrum of the V-type atomic ensemble. Meanwhile, the $\Lambda$ configuration does not show a such process. According to our results, in the appearance of the transparency window, the position of movable mirror changes significantly. (paper)