Quantum repeater using three-level atomic states in the presence of dissipation: stability of entanglement

Abstract

In this paper we want to investigate the possibility of transferring entanglement to two three-level separable atomic states over long 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 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 sources and initial interaction time are evaluated on the negativity and success probability of the processes. It is shown that, 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. In addition, increasing the initial interaction time has a constructive effect on the negativity in all considered cases. The oscillations of negativity are destroyed as time goes on and the produced entanglement becomes stable. 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 properly achieved while atomic and field dissipations are taken into account.