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Abstract
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In this paper, a Hamiltonian model that includes interaction of two coupled two-level atoms with a non-degenerate parametric amplifier in a cavity is introduced. By using the two-mode squeezing operator and under a certain condition, the introduced Hamiltonian is reduced to a generalized Jaynes{Cummings Hamiltonian. The constants of motion of system imply the existence of a decomposition of the system's Hilbert space H into 28 a direct sum of three infinite dimensional sub-spaces, as H = H(1) + H(2) + H(3). This decomposition enables us to study ground and thermally induced entanglement between the atoms in each of the sub-spaces as well as whole Hilbert space. The effect of atom-atom and atom-photon couplings on the degree of ground state and thermal entanglement are also investigated using the concurrence measure. It is found that in the subspaces H(1) and H(3) for all experimental values of parameters of the system, the atoms are disentangled. It is also observed that in the total space H the ground state entanglement is always zero, while in the subspace H(2) it is at its maximum value. Moreover, it is found that in the subspace H(2) thermal entanglement between the atoms is robust against temperature.
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