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arXiv:0908.4337 · Journal of Physics B Atomic Molecular and Optical Physics

Some entanglement features of a three-atom Tavis–Cummings model: a cooperative case

M Youssef, NASSER METWALLY, A.‐S. F. Obada

Published Apr 12, 2010• 16 citations
arXivHTMLPDF

Abstract

In this paper we consider a system of identical three two-level atoms interacting at resonance with a single-mode of the quantized field in a lossless cavity. The initial cavity field is prepared in the coherent state while the atoms are taken initially to be either in the uppermost excited state "$|eee>$" or The $\textmd{GHZ}$-state or the $\textmd{W}$-state. For this system we investigate different kinds of atomic inversion and entanglement, which arise between the different parts of the system due to the interaction. Also the relationship, between entanglement and some other nonclassical effects in the statistical properties, such as collapses and revivals in the atomic inversion where superharmonic effects appear, is discussed. The $Q$-functions for different cases are discussed. Most remarkably it is found that the $\textmd{GHZ}$-state is more robust against energy losses, showing almost coherent trapping and Schrödinger-cat states can not be produced from such state. Also the entanglement of $\textmd{GHZ}$-state is more robust than the $\textmd{W}$-state. Another interesting feature found is that the state which has no pairwise entanglement initially will have a much improvement of such pairwise entanglement through the evolution. Sudden death and sudden revival of atoms-pairwise entanglement are produced with the $\textmd{W}$-state.

DOI
10.1088/0953-4075/43/9/095501

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In this paper we consider a system of identical three two-level atoms interacting at resonance with a single-mode of the quantized field in a lossless cavity. The initial cavity field is prepared in the coherent state while the atoms are taken initially to be either in the uppermost excited state "∣eee>|eee>∣eee>" or The GHZ\textmd{GHZ}GHZ-state or the W\textmd{W}W-state. For this system we investigate different kinds of atomic inversion and entanglement, which arise between the different parts of the system due to the interaction. Also the relationship, between entanglement and some other nonclassical effects in the statistical properties, such as collapses and revivals in the atomic inversion where superharmonic effects appear, is discussed. The QQQ-functions for different cases are discussed. Most remarkably it is found that the GHZ\textmd{GHZ}GHZ-state is more robust against energy losses, showing almost coherent trapping and Schrödinger-cat states can not be produced from such state. Also the entanglement of GHZ\textmd{GHZ}GHZ-state is more robust than the W\textmd{W}W-state. Another interesting feature found is that the state which has no pairwise entanglement initially will have a much improvement of such pairwise entanglement through the evolution. Sudden death and sudden revival of atoms-pairwise entanglement are produced with the W\textmd{W}W-state.
Abstract In this paper, we demonstrate the exact solution of the nonstationary Schrodinger equation for the Tavis–Cummings model, in which three identical two-level atoms (qubits) are prepared in an arbitrary superposition of 8 Hilbert space vectors and which resonantly interact with a coherent resonator field mode of any intensity. The exact solution was used to calculate the parameters of atom–atom and atom-field entanglement: linear entropy, pairwise and three-particle negativity, and population inversion of three atoms. The results of computer modeling have shown that the degree of correlation between the atoms and the resonator field can significantly depend on the initial state of the atoms. Separable, biseparable, and genuine entangled W -type states demonstrate a high rate of energy exchange between atoms and the resonator field mode and the effect of sudden death of pairwise entanglement of atoms. On the contrary, all GHZ-states exhibit stable pairwise and three-particle entanglement between atoms and a slow rate of energy exchange between atoms and the resonator field mode. We also demonstrate the effect of the sudden death of three-particle entanglement for various states of atoms, the collapse and revival of the Rabi oscillations of the population inversion of three atoms, and the effect of the transition of entanglement from a subsystem of atoms to the total system. These results can be used for optimal operation of quantum networks.
The pairwise entanglement dynamics in a multipartite system consisting of three two-level atoms A, B, C and a single-mode cavity field a is studied via negativity. Three atoms are arranged in such a way that atoms BC are embedded in and locally interact with the cavity while atom A is located in a spatially separate place outside of the cavity. Initially, atom-pair AB is prepared in a Bell-like state while atom C in a superposition of ground and excited state, |gC〉 and |eC〉. It shall be shown that all the pairwise negativities of the total system including atoms and cavity undergo qualitatively different evolutions. The so-called entanglement sudden death is observed for atom-pair AB under certain conditions and the entanglement transfer among all the possible degrees of freedom of the whole system is also discussed.
The Jaynes-Cummings model of a single two-level atom interacting with a quantized single-mode coherent field generates at the half-revival time a dynamically disentangled atom-field state. At such times, the field is in asymptotically pure Schrödinger cat state, a macroscopic superposition of distinct field eigenmodes. In this paper we address the problem of field purity when a second atom is allowed to interact with the cavity mode and becomes entangled with the first atom via their mutual cavity field with which they interact. We employ the collective Dicke states to describe the cooperative effects on the entanglement and show that the second atom spoils the purity of the field state except for special cases of the atom-field coupling or of initial conditions.
We have studied entanglement evolution and transfer in a double Tavis-Cumming model where two pairs of entangled two-level atoms AB and CD interact with two single-mode cavity fields a and b. We show that the Bell-like initial state of atoms AB can exhibit entanglement sudden death which should be independent of the initial entanglement of atoms CD. Also, we show that the initial entanglement of one atomic pair can be transferred into another pair, as well as the possible subsystems, that become entangled during evolution.
We investigate the time evolution of pairwise entanglement between two Tavis–Cummings atoms for various entangled initial states, including pure and mixed states. We find that the phenomenon of entanglement sudden death behaviors is distinct in the evolution of entanglement for different initial states. What deserves mentioning here is that the initial portion of the excited state in the initial state is responsible for the sudden death of entanglement, and the degree of this effect also depends on the initial states.
We investigate the entanglement dynamics of two atoms interacting with a single-mode cavity field within the Tavis-Cummings model in the presence of noise. The atoms are initially prepared in either pure Bell states or mixed Werner states, allowing a direct comparison of pure- and mixed-state entanglement. The cavity field is described by generalized single-mode squeezed coherent thermal states, incorporating both thermal and quantum noise effects. Atom-atom and atom-field entanglement are quantified using concurrence and negativity, respectively. We analyze entanglement sudden death and revival, and examine how Ising-type coupling, dipole-dipole interaction, Kerr nonlinearity, and detuning modify the entanglement dynamics. Our results show that thermal photons generally suppress entanglement and enhance sudden death, while squeezing counteracts these effects. The influence of nonlinearities and interatomic interactions depends sensitively on the purity of the initial atomic state, leading to qualitatively different behaviors for Bell and Werner states.