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Dinâmica do emaranhamento num sistema tripartite

Manoel Pedro de Araujo

Published Aug 3, 2010• 0 citations
OpenAlex

Abstract

The proposal of this work is to study the bipartite entanglement between two constituents of a tripartite closed system, in the sense that there is no energy loss. The system consists of a pair of two-level atoms with equal transitions and one electromagnetic field mode in a cavity, with one of the atoms interacting with the field mode via Jaynes-Cummings interaction.We study the time evolution of entanglement between the two atoms, quantified by Wootters concurrence. The influence of initial state of the field in the appearance of singularities in this time evolution is discussed. Since concurrence is hard to determine experimentally, wedefine two directly measurable observables which, for the special initial conditions we study, can follow the entanglement behavior: the correlation operator, given by the product of the population inversions, and the Bell operator. We study the effects of initial states given bysuperpositions of two Fock states

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The proposal of this work is to study the bipartite entanglement between two constituents of a tripartite closed system, in the sense that there is no energy loss. The system consists of a pair of two-level atoms with equal transitions and one electromagnetic field mode in a cavity, with one of the atoms interacting with the field mode via Jaynes-Cummings interaction.We study the time evolution of entanglement between the two atoms, quantified by Wootters concurrence. The influence of initial state of the field in the appearance of singularities in this time evolution is discussed. Since concurrence is hard to determine experimentally, wedefine two directly measurable observables which, for the special initial conditions we study, can follow the entanglement behavior: the correlation operator, given by the product of the population inversions, and the Bell operator. We study the effects of initial states given bysuperpositions of two Fock states
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.
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 propose an experimental setup, feasible with present day technology, involving two highquality- factor cavities, one Ramsey zone and a two-level atom which interacts with them. The dynamics in the cavities is modeled by a dissipative dispersive Jaynes-Cummings model. Analytical expresions for the evolution superoperator in each part of the proposed setup and for the concurrence between the atom and the first cavity are given, and the pairwise entanglement of the subsystems is calculated numerically. We consider initial separable states given by the tensor product of a superposition of the two atomic relevant states and coherent states for the fields. We show that for realistic model parameters (including dissipation), when the dissipation rates are smaller than the dispersive frequencies (the ratio between the squared vacuum Rabi frequencies and the detunings), the final state of the cavity fields remains entangled.
An open quantum bipartite system consisting of two independent two-level atoms interacting nonlinearly with a two-mode electromagnetic cavity field is investigated by proposing a suitable non-Hermitian generalization of the Hamiltonian. The mathematical procedure of obtaining the corresponding wave function of the system is clearly given. Pancharatnam phase is studied to give a precise information about the required initial system state, which is related to artificial phase jumps, to control the degree of entanglement (DEM) and get the highest concurrence. We discuss the effect of time-variation coupling, and dissipation of both atoms and cavity. The effect of the time-variation function appears as frequency modulation (FM) effect in the radio waves. Concurrence rapidly reaches the disentangled state (death of entanglement) by increasing the effect of field decay. On the contrary, the atomic decay has no effect.
A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes–Cummings model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom–cavity couplings and off-resonant interactions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin-correlated and anti-correlated Bell states Φ and Ψ, a full, periodic and directed transfer of entanglement into a specific qubit pair is possible, for resonant interactions, depending on the choice of relative couplings. Furthermore, entanglement transfer and sudden death (ESD) can be prevented using off-resonant interactions, although for some initial states, detunings will trigger an otherwise frozen entanglement, to allow a full entanglement transfer.
We examine the dynamics of bipartite quantum entanglement between a two-level atom and the electromagnetic field. We begin with the Jaynes-Cummings model with a single field mode and examine in detail the exact time evolution of entanglement, including cases where the atomic state is initially mixed and the atomic transition is detuned from resonance. We then explore the effects of other nearby modes by calculating the exact time evolution of entanglement in more complex systems with two, three, and five field modes. For these cases we can obtain exact solutions which include the strong-coupling regime. Finally, we consider the entanglement of a two-level atom with the infinite collection of modes present in the intracavity field of a Fabre-Perot cavity. In contrast to the usual treatment of atom-field interactions with a continuum of modes using the Born-Markov approximation, our treatment in all cases describes the full non-Markovian dynamics of the atomic subsystem under general couplings. Only when an analytic expression for the infinite mode case is desired do we need to make a weak coupling assumption which at late times approximates Markovian dynamics.