Atom–atom entanglement via coherent photons in a nonlinear optical cavity

In the present article, dynamics of entanglement between two different two-level atoms, as nonidentical qubits, via monochromatic coherent photons is explored. The atoms are embedded in an optical lossless cavity filled with a centrosymmetric dielectric. A conserved (Casimir) operator, i.e. a dynamic integral of motion, is introduced to decompose the matrix representation of the total atom–photon Hamiltonian into direct sum of irreducible blocks. Using the eigenvalues and eigenvectors of the blocks, the time evolution unitary operator of the system is computed. The time-dependent atomic density operator is then calculated by partial tracing of atom–field density operator over photonic states for both initially separable and maximally entangled atomic states. The partially transposed atomic density operator, with respect to one of the atomic subsystems, is finally used to determine the negativity as an entanglement quantifier. Our results indicate that the robust entanglement is observed when the initial maximally atomic entangled state is applied. Furthermore, as Kerr-type coupling (arising from the third-order susceptibility of the centrosymmetric dielectric) increases it is shown that the entanglement enhances. In addition, effects of the initial atomic state preparation, the atom–photon structure parameters as well as field intensity on the entanglement birth and death are also addressed.