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Entanglement transfer between bipartite systems

The problem of a controlled transfer of an entanglement initially encoded into two two-level atoms that are successively sent through two single-mode cavities is investigated. The atoms and the cavity modes form a four qubit system and we demonstrate under which conditions the initial entanglement encoded into the atoms can be completely transferred to other pairs of qubits. We find that in the case of a nonzero detuning between the atomic transition frequencies and the cavity mode frequencies, no complete transfer of the initial entanglement is possible to any of the other pairs of qubits. In the case of exact resonance and equal coupling strengths of the atoms to the cavity modes, an initial maximally entangled state of the atoms can be completely transferred to the cavity modes. The complete transfer of the entanglement is restricted to the cavity modes only with the transfer to the other pairs being limited to up to 50%. We have found that the complete transfer of an initial entanglement to other pairs of qubits may take place if the initial state is not the maximally entangled state and the atoms couple to the cavity modes with unequal strengths. Depending on the ratio between the coupling strengths, the optimal entanglement can be created between the atoms and one of the cavity modes.