Exploring entanglement dynamics in an optomechanical cavity with a type-V qutrit and quantized two-mode field

In this work, the main objective is to measure the degree of interaction of a type-V qutrit with a two-mode quantized field in an optomechanical cavity. To achieve this objective, we first deduce the Hamiltonian in the interaction picture to identify the oscillatory terms. Using the Coarse-Grained Method (CGM), we obtain the effective Hamiltonian analytically. By selecting initial conditions for the atom, the two-mode field, and the moving mirror, we can determine the state vector of the entire system through a first-order approximation of the effective Hamiltonian. With this information, we proceed to solve the Schrödinger equation, generating a coupled set of differential equations that is solved numerically based on the initial conditions. In this context, the atomic von Neumann entropy allows us to obtain the temporal evolution of the degree of entanglement of the qutrit in the cavity and the atomic population inversion. The results indicate that entanglement in this tripartite system, composed of the qutrit and the mirror-field subsystems, as well as the population inversion, can be manipulated by the initial state conditions of the system, the qutrit-field and mirror-field coupling coefficients, the pump field, and the dissipation rates of the two-mode field and the movable mirror, respectively.