Aplicação das funções de quase-probabilidade no estudo da dinamica de emaranhamento




Entanglement dynamics of two ideal bipartites systems is analyzed using reduced linear entropy and quasiprobability distribution functions in the semiclassical regime.Two models are studied: the quartic bidimensional oscillator and the Dicke ?s Maser model. The first one describes the propagation of two monochromatic field modes in a Kerr medium, and the second describes the interaction of one mode of electromagnetic field with a collection of N non-interacting two-levels atoms. In the first model, besides the nonlinear interaction, we have considered the bilinear dipole-dipole interaction in the Rotating Wave Approximation. We have found the conditions at which the entanglement is reversible, and that recoherence times depend on the type of the chosen initial state. When a direct product of Fock states or a product of a coherent state and a Fock state are considered as initial states, bilinear interaction is the responsible for the entanglement. Whereas, if the initial state is a product of coherent states, the nonlinear interaction is the one responsible for the non-separability of the subsystems. In the limit of h ® 0, the loss of purity of the subsystems becomes practically irreversible. The behavior of reduced linear entropy and the Q-function allow us to show that there exist two regimens in time: before and after the beginning of the self-interferences.We have show that the time that separates the two regimes has the same dependence in the Planck ?s constant as the Ehrenfest time. In the Dicke ?s maser model,we have analyzed the temporal evolution of atomic Wigner function in the limit of many atoms for initial states where the two subsystems are prepared in coherent states. This allowed us to deepen our knowledge about the dynamics of the loss of purity based on the phase space classical dynamics. Our results about the dynamics of atomic Wigner function indicates that there is a clear relation between localization and delocalization of the atomic state,in terms of angular variables in Bloch sphere and the minima e maxima of the reduced linear entropy


caos quantico distribuição (probabilidades) sistemas não-lineares matriz de densidade

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