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

Abstract

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 an atomic Bell state, so that we have four separate pairs of maximally entangled states where . 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 non-entangled 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 the BSM method. Also, the effects of detuning, initial interaction time and coupling coefficient on the produced entanglement by the QED method are considered. Increasing (decreasing) of the detuning (interaction time) has a destructive effect on the swapped entanglement in asymmetric condition.