Dissipative quantum repeater

By implementing a quantum repeater protocol, our aim in this paper is the production of entanglement between two two-level atoms locating far from each other. To make our model close to experimental realizations, the atomic and field sources of dissipations are also taken into account. We consider eight of such atoms (\(1, 2, \ldots , 8\)) sequentially located in a line which begins (ends) with atom 1 (8). We suppose that initially the four atomic pairs \((i,i+1), i=1, 3, 5, 7,\) are mutually prepared in maximally entangled states. Clearly, the atoms 1, 8, the furthest atoms which we want to entangle them are never entangled, initially. To achieve the purpose of paper, at first, we perform the interaction between the atoms (2, 3) as well as (6, 7) which results in the entanglement creation between (1, 4) and (5, 8), separately. In the mentioned interactions, we take into account spontaneous emission rate (\(\varGamma \)) for atoms and field decay rate from the cavities (\(\kappa \)) as two important and unavoidable dissipation sources. In the continuation, we transfer the entanglement to the objective pair (1, 8) by two methods: (i) Bell state measurement and (ii) cavity quantum electrodynamics. The successfulness of our protocol is shown via the evaluation of concurrence as the well-established measure of entanglement between the two (far apart) qubits (1, 8). We also observe that if one chooses the cavity and the atom such that \(\kappa =\varGamma \) holds, the effect of dissipations is effectively removed from the entanglement dynamics in our model. In this condition, the time evolutions of concurrence and success probability are regularly periodic. Also, concurrence and success probability reach their maximum values in a large time interval by decreasing the detuning in the presence of dissipation.