Eur. Phys. J. Plus (2017) 132: 3
https://doi.org/10.1140/epjp/i2017-11281-7

Regular Article

On the entanglement swapping by using the beam splitter

¹ Faculty of Physics, Shahid Bahonar University of Kerman, Kerman, Iran
² Department of Physics, Estahban higher education center, Estahban, Iran
³ Atomic and Molecular Group, Faculty of Physics, Yazd University, Yazd, Iran
⁴ Research Group of Optics and Photonics, Yazd University, Yazd, Iran

^* e-mail: mktavassoly@yazd.ac.ir

Received: 17 October 2016
Accepted: 5 December 2016
Published online: 12 January 2017

Abstract

In this paper, we outline three different setups for the entanglement swapping process. The common aspect of these setups is generation of the atom-field entangled state in the optical cavity and using a 50 : 50 beam splitter to swap the entanglement to the new subsystems. The first scheme contains two distinct atom-field entangled states (, j = 1, 2), each previously generated via the Jaynes-Cummings model. According to our proposal, once the two field states are emitted into the beam splitter and when the field F ₁ is detected, the two participating atoms, without detecting F ₂ , form an entangled state. Therefore, the entanglement swapping from “A _j -F _j ”, j = 1, 2 to the two atoms appropriately occurs. The second scheme contains an entangled state of “ A ₁ - F ₁ ” as well as a cavity field F ₂ , in which the entangled state is generated by using two Ramsey zones and the atom-field interaction in the large detuning regime. Injecting the fields F ₁ and F ₂ into the beam splitter, operating an inverse Hadamard gate on the atom A ₁ and the atom-field interacted subsystem “ A ₁ - F ₁ ” in the large detuning regime, helps us transfer the entanglement to the “ A ₁ - F ₂ ” subsystem. In the final scheme, the atom A ₁ is initially entangled with the cavity field F ₁ via the atom-field interaction in the optical cavity. Also, the other field F ₂ is considered in the coherent state . Injecting the state of the two fields into the 50 : 50 beam splitter, one arrives at an entangled state between A ₁ and F ₂ for small and large values of (a measure of the coherent field intensity). Accordingly, again the entanglement swapping takes place properly.