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International Journal of Modern Physics B

The influence of excitation number of photon-added coherent state field on the entanglement swapping process

M. Soltani, Mohammad Kazem Tavassoly, Razieh Pakniat

Published Jun 14, 2017• 4 citations
Publisher

Abstract

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].

DOI
10.1142/s0217979217501983

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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].
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.
Abstract In this study, we present two protocols for entanglement swapping and quantum teleportation using an optomechanical cavity, wherein the moving mirror behaves as an auxiliary mode. The initial state of the system comprises two distinct entangled state pairs: one between atoms 1 and 2 and the other between cavity fields 3 and 4 (which are prepared in an entangled state of number and coherent states). By interacting the atom 2, field 3 and the auxiliary mode of the moving mirror, initially in the ground state ∣0〉 m , inside the optomechanical cavity, and applying the detection method, a tripartite entangled state is generated via entanglement swapping process. As a result, the initial atom 1–atom 2 and also field 3–field 4 entanglements are converted into the tripartite system, atom 1, field 4, and the auxiliary mode. We then evaluate and analyze the influence of the optomechanical coupling coefficient on the significant quantities in the entanglement swapping model, such as the success probability of the detection process, the fidelity, and the linear entropy (as a measure of entanglement). Finally, we demonstrate that the optomechanical cavity can be employed to teleport a bipartite entangled state with perfect fidelity by utilizing a quantum channel in the form of an unknown tripartite entangled state.
The effects of a chaotic field on the entanglement dynamics in a system of interaction of a two-level atom with a single-mode cavity field prepared in a Glauber–Lachs state were investigated in the framework of the Jaynes–Cummings model. We found that the entanglement is a non-monotonic function of the ratio of the mean numbers of thermal photons and coherent photons or, equivalently, the degree of initial mixedness of the system. There is an optimal value of this ratio up to which thermal photons contribute increasingly to the entanglement and after which they weaken the strength of the entanglement.
In this paper, we study the quantum teleportation of an unknown atomic state based on the two-photon Jaynes-Cummings model, consisting of an effective two-level atom with a two-mode field in the generalized photon-added pair coherent state (GPAPCS). By applying the detecting method, we use a scheme that includes two two-level atoms and a cavity field to teleport the unknown atomic state from a sender to a receiver. The results show that the number of photons added to the field and the intensity of the initial field influence the average fidelity and success probability of the teleportation process. The time-evolution dependence of the average fidelity is also considered and compared for the field in the pair coherent state and in the GPAPCS.