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Acta Physica Sinica

Entanglement swapping in the process of two-level atoms interacting with cavity fields of coherent states*

Lai Zhen-jiang, Yang Zhi-yong, Jintao Bai, Sun Zhong-yu, (1)河南师范大学物理系,新乡 453007;西北大学光子学与光子技术研究所,光电子技术省级重点实验室，西安 710069; (2)西安交通大学电子与信息工程学院,西安 710049; (3)西北大学光子学与光子技术研究所,光电子技术省级重点实验室，西安 710069

Published Jan 1, 2004• 2 citations
Publisher

Abstract

From the viewpoint of quantum information theory, a multiatom and muticavity system was investigated. In the system the interaction between the atoms and the fi elds in the cavities is described by the intensity-dependent coupling Jaynes-Cummings model. It is found that the atomic maximal entangled state can be transformed into the maximal odd-even-like coherent entangled state, whereas the maximal odd-even-like coherent entangled state also can be transfor med into the atomic maximal entangled state.

DOI
10.7498/aps.53.3733

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

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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].

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Iranian Journal of Physics Research•Sep 1, 2025•0 citations
From the viewpoint of quantum information theory, a multiatom and muticavity system was investigated. In the system the interaction between the atoms and the fi elds in the cavities is described by the intensity-dependent coupling Jaynes-Cummings model. It is found that the atomic maximal entangled state can be transformed into the maximal odd-even-like coherent entangled state, whereas the maximal odd-even-like coherent entangled state also can be transfor med into the atomic maximal entangled state.
From the viewpoint of complete quantum theory,the process of the nonresonant interaction of atoms with cavity fields by intensity-dependent coupling was analyzed in the joint system consisting of multi-atom and multi-cavity.It is found that the quantum entanglement information can be completely interchanged between the atomic maximal entangled state and the maximal odd-even-like coherent entangled state by controlling the time of atoms interacting with cavity fields and measuring the atom states just being out of cavity.The quantum information can be completely swap by properly limiting the detuning value.The procedures mentioned above show that the process of evolution is reversible within the close system.
The unresonant procedure of the interaction of atoms with cavity-field by intensity-dependent coupling was analyzed in the union system consisting of multi-atom and multi-cavity using of the complete quantum theory. The results show that through controlling the time of cavity-field interacting with atoms and measuring the atomic states just being out of cavity, the quantum entangled information can be completely exchange between the atomic maximal entangled state and the maximal like-odd-even coherent entangled state. The quantum information can be completely swapping transmit on account of properly confining the detuning value. The process above mentioned display that the evolution is opposite each other in the close system.
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.
In this research, we investigate the entanglement between two cavities, each consisting of a two-level atom and a deformed multi-photon field. The model used in this study is the deformed Jaynes-Cummings (DJC) model. A physical interpretation of the introduced model is that there are two separate cavities with Kerr-like environments, each containing a two-level atom and a non-deformed multi-photon field, where each atom interacts locally with its corresponding field. Generally, we assume that the coupling constants between the atoms and fields are unequal, and we also consider non-zero detuning. We prove that the simple rules applicable to symmetric cavities without detuning do not hold for asymmetric cavities. We will show that the presence of asymmetric cavities and detuning are factors that can be used to control entanglement. Additionally, we examine the effects of deformed fields (Kerr-like environments) on the temporal evolution of entanglement and demonstrate that they cause the entanglement to become more oscillatory. We will show that when the sign of entanglement changes, the temporal evolution of entanglement will be completely different. We consider two different initial states of the system and show that the temporal evolution of entanglement will differ for these two states. In fact, the temporal evolution of entanglement depends on the initial state of the system. To measure the entanglement, we use the concurrence parameter, where a value of one indicates maximum entanglement and a value of zero indicates no entanglement. We will also show that an initial maximum atomic entanglement can be transferred to another pair of qubits, and the type of this qubit pair depends on whether the ratios of the coupling constants are even or odd. We demonstrate that for odd ratios of coupling constants, the initial maximum atomic entanglement can be completely transferred to the fields at a specific time.