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Physica Scripta

Entanglement swapping in the two-photon Jaynes–Cummings model

A.D. dSouza, Wesley Bueno Cardoso, Ardiley Torres Avelar, B. Baseia

Published Dec 1, 2009• 16 citations
Publisher

Abstract

In the present work, we study the entanglement swapping via the two-photon process without explicitly using the Bell-state measurement. We employ the appropriate ‘full two-photon Hamiltonian approach’ instead of the ‘effective Hamiltonian approach’ used in recent schemes. We obtain entanglement swapping with 94.7% fidelity for maximally entangled states by conveniently choosing the atom–field interaction time. The success probability is also considered.

DOI
10.1088/0031-8949/80/06/065009

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In the present work, we study the entanglement swapping via the two-photon process without explicitly using the Bell-state measurement. We employ the appropriate ‘full two-photon Hamiltonian approach’ instead of the ‘effective Hamiltonian approach’ used in recent schemes. We obtain entanglement swapping with 94.7% fidelity for maximally entangled states by conveniently choosing the atom–field interaction time. The success probability is also considered.
In this work we have studied the two photon Jaynes-Cummings model to describe the interaction of a three-level atom in the configuration with a single-mode of a cativy-field. We have used the effetive and full microscopic Jamiltonian approach to compare the results obtained in these tow descriptions. We employed the two-photon Jaynes-Cummings model int the full microscopic Hamiltonian context to implement schemes to quantuam entanglement swapping, for approximate and conditional quantuam teleportation for an unknown atomic state, for a superposition of zero- and two photon states. Both schemes were implemented using no measurement in the Bell base states.
Recently we studied the effect of photon addition in the initial coherent field on the entanglement swapping which causes some improvements in the process [Soltani et al., Int. J. Mod. Phys. B 31, 1750198 (2017)]. In this paper, we investigate the influence of multiphoton transitions in the atom–field interaction based on the cavity quantum electrodynamics on the entanglement swapping and show its considerable constructive effect on this process. The presented model consists of two two-level atoms namely A1and A2and two distinct cavity fields F1and F2. Initially, the atoms are prepared in a maximally entangled state and the fields in the cavities are prepared in hybrid entangled state of number and coherent states, separately. Making the atom A2to interact with the field F1(via the generalized Jaynes–Cummings model which allows m-photon transitions between atomic levels in the emission and absorption processes) followed by their detection allows us to arrive at the entanglement swapping from the two atoms A1, A2and the two fields F1, F2to the atom–field A1–F2system. Then, we pay our attention to the time evolution of success probability of detecting processes and fidelity. Also, to determine the amount of entanglement of the generated entangled state in the swapping process, the linear entropy is evaluated and the effect of parameter [Formula: see text] concerning the multiphoton transitions on these quantities is investigated, numerically. It is observed that, by increasing the number of photons in the transition process, one may obtain considerable improvement in the relevant quantities of the entanglement swapping. In detail, the satisfactorily acceptable values 1 and 0.5 corresponding to success probability and fidelity are obtained for most of the times during observing of the above-mentioned procedure. We concluded that the presented formalism in this paper is much more advantageous than our presentation model in our earlier work mentioned above.
In this paper, we outline a scheme for the entanglement swapping procedure based on cavity quantum electrodynamics using the Jaynes–Cummings model consisting of the coherent and photon-added coherent states. In particular, utilizing the photon-added coherent states ([Formula: see text][Formula: see text][Formula: see text][Formula: see text], where [Formula: see text] is the Glauber coherent state) in the scheme, enables us to investigate the effect of [Formula: see text], i.e., the number of excitations corresponding to the photon-added coherent field on the entanglement swapping process. In the scheme, two two-level atoms [Formula: see text] and [Formula: see text] are initially entangled together, and distinctly two exploited cavity fields [Formula: see text] and [Formula: see text] are prepared in an entangled state (a combination of coherent and photon-added coherent states). Interacting the atom [Formula: see text] with field [Formula: see text] (via the Jaynes–Cummings model) and then making detection on them, transfers the entanglement from the two atoms [Formula: see text], [Formula: see text] and the two fields [Formula: see text], [Formula: see text] to the atom-field “[Formula: see text]-[Formula: see text]”, i.e., entanglement swapping occurs. In the continuation, we pay our attention to the evaluation of the fidelity of the swapped entangled state relative to a suitable maximally entangled state, success probability of the performed detections and linear entropy as the degree of entanglement of the swapped entangled state. It is demonstrated that, an increase in the number of excitations, [Formula: see text], leads to the increment of fidelity as well as the amount of entanglement. According to our numerical results, the maximum values of fidelity (linear entropy) 0.98 (0.46) is obtained for [Formula: see text], however, the maximum value of success probability does not significantly change by increasing [Formula: see text].