Ground state and thermal entanglement between two two-level atoms interacting with a nondegenerate parametric amplifier: Different sub-spaces

Abstract

In this paper, a Hamiltonian model that includes interaction of two coupled two-level atoms with a nondegenerate 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 [Formula: see text] into a direct sum of three infinite dimensional sub-spaces, as [Formula: see text]. 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 [Formula: see text] and [Formula: see text] for all experimental values of parameters of the system, the atoms are disentangled. It is also observed that in the total space [Formula: see text] the ground state entanglement is always zero, while in the subspace [Formula: see text] it is at its maximum value. Moreover, it is found that in the subspace [Formula: see text] thermal entanglement between the atoms is robust against temperature.