Thermal entanglement between two coupled two-level atoms in two-photon interacting with codirectional Kerr nonlinear coupler

In this paper, a Hamiltonian model that includes interaction of two two-level atoms with a codirectional Kerr nonlinear coupler via the Raman non-degenerate two-photon transition is introduced. The atomic interaction is assumed in the dipole-dipole form and the total system is also in thermal equilibrium with the environment. The total excitation number operator, as the constant of motion of system provides a decomposition of the Hilbert space of system into direct sums of invariant subspaces. As a result, the representation of the Hamiltonian becomes block-diagonal matrix. By diagonalizing each of blocks, we obtain eigenvalues and corresponding eigenstates of the Hamiltonian. Then we obtain thermal state of system in the whole Hilbert space and within its excitation subspaces. We quantify thermal entanglement between the atoms in the Hilbert space of system and within its excitation subspaces using the measure of concurrence. Finally, the effect of temperature and system parameters on the degree of thermal entanglement is investigated. The results show that in the subspaces with odd excitation number, the atomic thermal entanglement is thermally robust and remains constant.