Analysis of the behavior of entanglement parameters for the three-qubit Tavis-Cummings model with multiphoton processes

In this paper, we analyze in detail the dynamics of the negativity criterion, fidelity and concurrence fill for the Tavis-Cummings model in which three qubits are in a common single-mode ideal resonator and interact resonantly with the field mode via multiphoton processes. By solving the unsteady Schrödinger equation, we give analytic solutions for genuine entangled Werner- and Greenberger-Horn-Zeilinger states. It is shown that the multiplicity of photon transitions can significantly stabilize the genuine entangled states of both types. Key features in the dynamics pattern of the entanglement parameters are highlighted. We conclude that the negativity criterion is not suitable for describing the dynamics of entanglement of qubits in the case of three-qubit Greenberger-Horn-Zeilinger states. Main advantages of the concurrence fill over the negativity criterion are shown.