Long-lived genuine entangled of Werner and Greenberger-Horn-Zeilinger states in the three-qubit Tavis-Cummings thermal model with multiphoton processes

An exact solution for the evolution operator of the multiphoton three-qubit Tavis-Cummings model was found. On this basis, the entanglement dynamics and the phenomenon of entanglement sudden death for entangled initial W-, GHZ-, and GHZ-like qubit states and the thermal state of the resonator were studied by means of pairwise negativity and fidelity. The results of entanglement parameters calculations showed that in the nonlinear multiphoton processes, the atomic entanglement is stronger than in the linear one-photon process. We also obtained that the so-called sudden death phenomenon occurs only for some kind of initial qubit states and some thermal noise intensities, i.e. the phenomenon is sensitive to the initial conditions. The length of the time interval for the zero entanglement is dependent on not only the initial qubit states but also the photon transition multiple. We also showed that for large values of the multiple, only one W-type initial state and one GHZ-like initial state are the long-lived and maximally persistent and robust states.