Entangling operations in nonlinear two-atom Tavis-Cummings models

We derive an analytical approximate solution of the time-dependent state vector in terms material Bell states and coherent field for a generalized two-atom Tavis-Cummings model with nonlinear intensity-dependent matter-field interaction. Using this solution, we obtain simple expressions atomic concurrence purity order to study entanglement system at specific interaction times. show how implement entangling operations through measurement field. illustrate these can lead complete measurement. Furthermore, when considering two orthogonal as levels third qubit, it is possible unitary three-qubit gate capable generating authentic tripartite entangled such Greenberger-Horne-Zeilinger $W$ state. As example generic model, present ion-trap setting employing quantized mode center-of-mass motion instead photonic field, showing that implementation realistic from intrinsic interactions indeed possible.