Dynamics of different entanglement measures of two three-level atoms interacting nonlinearly with a single-mode field

摘要

In this paper, we present a model which exhibits two identical $\Xi$-typethree-level atoms interacting with a single-mode field with $k$-photontransition in an optical cavity enclosed by a Kerr medium. Considering fullnonlinear formalism, it is assumed that the single-mode field, atom-fieldcoupling and Kerr medium are all $f$-deformed. By using the adiabaticelimination method, it is shown that, the Hamiltonian of the considered systemcan be reduced to an effective Hamiltonian with two two-level atoms and$f$-deformed Stark shift. In spite of the fact that, the system seems to becomplicated, under initial conditions which may be prepared for the atoms(coherent superposition of their ground and upper states) and the field(coherent state), the explicit form of the state vector of the entire system isanalytically obtained. Then, the entanglement dynamics between differentsubsystems (i.e. "field-two atoms", "atom-(field+atom)" and "atom-atom") areevaluated through appropriate measures like von Neumann entropy, tangle andconcurrence. In addition, the effects of intensity-dependent coupling, deformedKerr medium, detuning parameter, deformed Stark shift and multi-photon processon the considered entanglement measures are numerically analyzed, in detail. Itis shown that the degree of entanglement between subsystems can be controlledby selecting the evolved parameters, suitably. Briefly, the Kerr medium highlydecreases the amount of different considered measures of entanglement,especially for two-photon transition. This destructive effect preserves evenwhen all other parameters are present, too. Furthermore, we find that theso-called entanglement sudden death and birth can occur in the atom-atomentanglement.