Abstract. In this paper, we investigate the possibility of the entanglement swapping between two independent nonperfect cavities consisting of an atom with finite lifetime of atomic levels (as two independent sources of dissipation) which interacts with a quantized electromagnetic field in the presence of detuning and Kerr medium. In fact, there is no direct interaction between the two atoms, therefore, no entanglement exists between them. We use the Bell state measurement performing on the photons leaving the cavities to swap the entanglement stored between the atom-fields in each cavity into atom-atom. Our motivation is arisen from the fact that two-qubit entangled states are of enough interest for quantum information science and technologies. We discuss the effect of initial state of the system, detuning parameter, the Kerr medium and the two dissipation sources on the swapped entanglement to atom-atom. We interestingly find that when the atomic decay rates and photonic leakages from the cavities are equal, our system behaves as an ideal system with no dissipation. Our results show that it is possible to create a long-living atom-atom maximally entangled state in the presence of Kerr effect and dissipation; we determine these conditions in detail and also establish the final atom-atom Bell state. PACS

In this paper we study the production of entanglement between two atoms which are 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 Bell state, 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 the atomic pair (1, 8), while these two distant atoms have no interaction. By performing the interaction between adjacent nonentangled atomic pairs (2, 3) as well as (6, 7), each pair with a two-mode quantized field, the entanglement is produced between atoms (1, 4) and (5, 8), respectively. Finally, by applying an appropriate Bell state measurement (BSM) on atoms (4, 5) or performing an interaction between them with a single-mode field (quantum electrodynamic: QED method), the qubit pair (1, 8) becomes entangled and so the quantum repeater is successfully achieved. This swapped entanglement is then quantified via concurrence measure and the effects of coupling coefficients and detuning on the concurrence and success probability are numerically investigated. The maxima of concurrence and success probability and the corresponding time periods have been decreased by increasing the detuning in asymmetric condition in BSM method. Also, the effects of detuning, initial interaction time and coupling coefficient on the produced entanglement by QED method are considered. Increasing (decreasing) of the detuning (interaction time) has destructive effect on the swapped entanglement in asymmetric condition.

The aim of this paper is to swap the entanglement between two separate long distant locations. The well-known entangled coherent states as two-mode continuous-variable states are very interesting in quantum teleportation and entanglement swapping processes. To make our investigation more realistic, by using such entangled states as the building block of our quantum repeater protocol, the effect of decoherence on the swapped entanglement is also considered. We explicitly establish our model for four locations, moreover, we find that our model can be extended to 2 N locations, where N = 3, 4, • • • . Consequently, we could introduce this model as a quantum repeater which is helpful for entanglement swapping to enough long distances.

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In this paper we want to investigate the possibility of transferring entanglement to two three-level separable atomic states over large distance using the quantum repeater protocol. In detail, our model consists of eight Λ-type three-level atoms where only the pairs (1,2), (3,4), (5,6) and (7,8) are prepared in maximally entangled states. Performing suitable interaction between non-entangled three-level atoms (2,3) and (6,7) in two-mode cavities with photon leakage rates κ, κ ′ in the presence of spontaneous emission leads to producing entanglement between atoms (1,4) and (5,8), separately. Finally, the entanglement between atoms (1,8) is successfully produced by performing interaction between atoms (4,5) while spontaneous emission is considered in a dissipative cavity. In the continuation, the effects of detuning, dissipation and initial interaction time are considered on negativity and success probability of the processes. The maxima of negativity are decreased by increasing the detuning, in most cases. Also, the time evolution of negativity is non-periodic in the presence of dissipation. Increasing the initial interaction time has a constructive effect on negativity in all considered cases. The oscillations of negativity are destroyed as time goes on and the produced entanglement is stabled. The success probability of entangled state of atoms (1,8) is tunable by controlling the detuning and dissipation. We show that via justifying the involved parameters one can arrive at conditions in which the decoherence effects are fully disappeared; as a result an ideal quantum repeater can be achieved while atomic and field dissipations are taken into account.