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Journal of Modern Optics

Violation of Mermin–Ardehali–Belinksii–Klyshko inequality in the three-Jaynes–Cummings model

LU Dao-ming

Published Oct 25, 2018• 4 citations
Publisher

Abstract

In this paper, we consider the situation that three identical two-level atoms are separately trapped in the three single-mode cavities. Each atom resonantly interacts with cavity via a one-photon hopping. The dynamics of nonlocality in the system is investigated via Mermin–Ardehali–Belinksii–Klyshko inequality. The results show that when three atoms are initially in W state and three-cavity fields are in vacuum states both the quantum state of three atoms and that of three cavities all display nonlocality On the other hand, when three atoms are initially in Greenberger–Horne–Zeilinger state and three-cavity fields are in vacuum states, the quantum state of three atoms and that of three cavities all do not display nonlocality.

DOI
10.1080/09500340.2018.1537406

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In this paper, we consider the situation that three identical two-level atoms are separately trapped in the three single-mode cavities. Each atom resonantly interacts with cavity via a one-photon hopping. The dynamics of nonlocality in the system is investigated via Mermin–Ardehali–Belinksii–Klyshko inequality. The results show that when three atoms are initially in W state and three-cavity fields are in vacuum states both the quantum state of three atoms and that of three cavities all display nonlocality On the other hand, when three atoms are initially in Greenberger–Horne–Zeilinger state and three-cavity fields are in vacuum states, the quantum state of three atoms and that of three cavities all do not display nonlocality.
Entanglement and nonlocality, two most striking features of quantum mechanics, are fundamental resources for quantum information processing. They play an important role in quantum information processing. Therefore, studying the dynamics of quantum nonlocality and entanglement is of importance for both fundamental research and practical applications. In this paper we consider the case that three identical two-level atoms are trapped respectively in the three separated equidistance single-mode cavities, which are placed at the vertices of an equilateral triangle and are coupled by three fibers. Each atom resonantly interacts with cavity via a one-photon hopping. The evolution of the state vector of the system is given by solving the schrodinger equation when the total excitation number of the system equals one. The dynamics of nonlocality in the system is investigated via Mermin-Ardehali-Belinksii-Klyshko (MABK) inequality. By the numerical calculations, the MABK inequality is studied when the initial state vector of three atoms is W state or the initial state vector of three cavities is also W state. The influence of cavity-fiber coupling constant on the MABK inequality is discussed. The evolution curves of the MABK parameters Ba and Bc are plotted. The curves show that Ba and Bc both display periodic oscillations, and their oscillation frequencies all increase with the increase of cavity-fiber coupling constant. Ba and Bc are both larger than 1 when the scaling time gt takes a certain value. The results show that the quantum state of three atoms or that of three cavities displays nonlocality. On the other hand, the nonlocality of three-atom quantum state is strengthened with the increase of cavity-fiber coupling constant.
We study the Bell-nonlocality dynamics of three remote atoms, two of which are trapped in one single-mode cavity and the third atom is trapped in another remote single-mode cavity. The interactions between the atoms and the cavity modes are studied via Tavis Cummings and Jaynes Cummings models. Here, the two single-mode cavities are introduced to simulate two different enviroments of the three atoms. The tripartite nonlocal correlations are studied in terms of the Svetlichny inequality and the WWZB inequality, respectively. The results show that the tripartite Bell-nonlocality sudden death will occur for the W state and GHZ state initial conditions. The detailed results demonstrate that the tripartite nonlocality of GHZ state is more robust than that of W state when suffering from the effect of environments.
In this paper we consider the situation that four identical two-level atoms are separately trapped in coupled single-mode optical cavities and each atom resonantly interacts with cavity via a one-photon hopping. The three-body entanglement dynamics in each cavity is studied. The influences of atom-cavity coupling constant on the three-body entanglement are discussed. The results obtained using the numerical method show that the three-body entanglement displays the collapse-revival phenomena when atom-cavity coupling constant is larger than a fixed value. On the other hand, the three-body entanglement is the result of the coherent superposition of the two-body entanglements.
In this paper we consider the situation that three identical two-level atoms resonantly interact with three distant single-mode optical cavities via a one-photon hopping separately.Three atoms are in like-GHz state and therr optical cavities are all in vacuum state initially.Using the Jaynes-Cummings,the time evolution of the system is given.We adopt the entanglement tensor approach to quantify the degree of entanglement.The tripartite entanglement dynamics among three atoms and the entanglement dynamics between two atoms are studied.The influence of atomic states initially on tripartite entanglement among atoms and two-body entanglement between two atoms are discussed.The results obtained using the numerical method show:first,the time evolution of tripartite entanglement displays the periodic oscillation behavior and its oscillation period is not realted with the initial degree of entanglement among atmos;second the peak and mean of entanglement measures E3 and F2 incease with increasing of the initial degree of entanglement among atmos,which means that the larger the initial degree of entanglement among atoms,the layer the tripartite entanglement among atoms and the two-body entanglement between atoms;third,the phenomenon of sudden death of entanglement between two atoms occurs,and the length of the death time interval decreases with increasing of the initial degree of entanglement among atoms.This shows that the length of the death time interval of two-body entanglement can be decreased by selecting initially atomic state with high degree of entanglement among atoms.
We study the genuine tripartite nonlocality of some qubit states in a triple JCM. In this model, each atom state (A, B or C) was initially prepared with an independent cavity (a, b or c). By using two kinds of GHZ-like states as the atomic initial states, we investigate the genuine tripartite nonlocality as the time evolutions for the non-interaction three-qubit subsystems. We also study the genuine tripartite nonlocality of the subsystems by using the Svetlichny inequality. For the subsystems of three atoms ABC and three cavity modes abc, we show that they are genuinely nonlocal at certain period intervals of time. The states of all the other inequivalent subsystems satisfy the Svetlichny inequality for two types of GHZ-like states.
We study the dynamics of a two-level atom interacting with a single mode of a damped cavity at 0 K when the cavity is initially in the vacuum state and the atom enters it in an arbitrary (pure or mixed) state. A complete analytical solution of this simple model is presented. On the basis of this solution we firstly investigate the pseudo-spin dynamics of the atom and the cavity field, secondly give an illustration of the Araki-Lieb theorem concerning the von Neumann entropies of interacting quantum systems and thirdly demonstrate the generation of entangled states of the atom and cavity field that are of interest in connection with the Bell inequalities.