Quantum Fisher information and entanglement of a dissipative hybrid optomechanical system with multi-photon transition

The fundamental concept of quantum Fisher information (QFI) evaluating the high sensitivity of a quantum state to parameter variations, plays a crucial role in the realm of parameter estimation theory. Here, we investigate the estimation precision of the mechanical oscillator decay rate in a hybrid optomechanical system by making use of the atomic quantum Fisher information. We also talk about entanglement and try to link this quantum feature with QFI. The considered quantum system contains a \(\Lambda \) $\mathrm{\Lambda }$ -type three-level atom interacting with two optical modes by multi-photon transition in the presence of different sources of the dissipation. Applying the effective non-Hermitian Hamiltonian, we get the explicit form of the state vector of the entire system analytically, with the help of the time-dependent Schrödinger equation. The obtained results show that the dynamics of the atomic QFI and entanglement can suitably be controlled by optomechanical and the atom-field coupling strengths, dissipation parameters and multi-photon transition. It can be seen that decreasing the coefficient of optomechanical coupling as well as the strength of atom-field coupling reduces the amount of QFI. Moreover, it is found that there exists a monotonic relation between the atomic QFI and the quantum entanglement in the absence of atomic decay and optical loss.