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In this paper we study the production of entanglement between two atoms whichare far from each other. We consider a system including eight two-level atoms(1; 2;... ; 8) such that any atom with its adjacent atom is in atomic Bellstate, so that we have four separate pairs of maximally entangled states (i; i+ 1) where i = 1; 3; 5; 7. Our purpose is to produce entanglement between theatomic pair (1, 8), while these two distant atoms have no interaction. Byperforming the interaction between adjacent nonentangled atomic pairs (2, 3) aswell as (6, 7), each pair with a two-mode quantized field, the entanglement isproduced between atoms (1, 4) and (5, 8), respectively. Finally, by applying anappropriate Bell state measurement (BSM) on atoms (4, 5) or performing aninteraction between them with a single-mode field (quantum electrodynamic: QEDmethod), the qubit pair (1; 8) becomes entangled and so the quantum repeater issuccessfully achieved. This swapped entanglement is then quantified viaconcurrence measure and the effects of coupling coeficients and detuning on theconcurrence and success probability are numerically investigated. The maxima ofconcurrence and success probability and the corresponding time periods havebeen decreased by increasing the detuning in asymmetric condition in BSMmethod. Also, the effects of detuning, initial interaction time and couplingcoeficient on the produced entanglement by QED method are considered.Increasing (decreasing) of the detuning (interaction time) has destructiveeffect on the swapped entanglement in asymmetric condition.

Quantum repeater protocol in mixed single- and two-mode Tavis-Cummings models