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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Transição de fase Superfluido-Isolante de Mott em redes ópticas via modelo de Jaynes-Cummings-Hubbard

Gomes, Clélio Brasil Cardoso 25 March 2013 (has links)
We study the phase transition super uid-Mott insulator in optical lattices through model Jaynes-Cummings-Hubbard using the fermion approximation. Initially we did a review of the Jaynes-Cummings model that is a model that describes the interaction between an atom with two levels and a quantized electromagnetic eld. Then we stu- died the properties of the phase transition super uid-Mott insulator (SF-MI) through the model Bose-Hubbard and we discuss the characteristics of the two quantum phases and the conditions for phase transition. Apply the model Jaynes-Cummings-Hubbard in order to study the in uence of topology of network Bravais linear, square, single cubic (SC), body-centered cubic (BCC) and face-centered cubic (FCC) in the phase transi- tion SF-MI to different numbers of excitation and different detuning values between the atom and the eld and we found that the Mott lobes and the critical hopping terms are not renormalizable only for the FCC network. But the regime from many excitations, the critical hopping is renormalizable to all networks and is independent of detuning. Then we study the Jaynes-Cummings-Hubbard model for a chain with the addition of the Kerr effect (nonlinear optical effect) through the approximation of fermions (FA). We observed that the Kerr effect does not cause large changes in the energy spectrum. However, the properties of the phase transition SF-MI undergoes signicant changes due to the Kerr effect. Another important feature which has been observed is that the Kerr effect favors the phase MI. / Estudamos a transi¸c ao de fase superfluido-isolante de Mott (SF-MI) em redes ´opticas via modelo Jaynes-Cummings-Hubbard utilizando a aproxima¸c ao de f´ermions. Inicialmente fazemos uma revis ao do modelo Jaynes-Cummings que descreve a intera¸c ao de um ´atomo de dois n´ıveis com um campo eletromagn´etico quantizado. Em seguida estudamos as propriedades da transi¸c ao de fase SF-MI no modelo Bose-Hubbard e discutimos as caracter´ısticas das duas fase qu anticas e as condi¸c oes para a transi¸c ao de fase. Aplicamos o modelo Jaynes-Cummings-Hubbard com a finalidade de estudarmos a influ encia da topologia das redes de Bravais linear, quadrada, c´ubica simples (SC), c´ubica de corpo centrado (BCC) e c´ubica de faces centradas (FCC) na transi¸c ao de fase SF-MI para diferentes n´umeros de excita¸c ao e diferentes valores de dessintonia entre o ´atomo e o campo e encontramos que os l´obulos de Mott n ao s ao renormaliz ´aveis apenas para a rede FCC. Mas no regime de muitas excita¸c oes, as redes BCC e FCC passam a ter o mesmo comportamento enquanto que as demais continuam com sua depend encia no n´umero de vizinhos. Em seguida, estudamos o modelo de Jaynes-Cummings-Hubbard para uma cadeia com a adi¸c ao do efeito tipo Kerr (efeito ´optico n ao-linear) atrav´es da aproxima¸c ao de f´ermions (FA). Observamos que o efeito tipo Kerr n ao provoca grandes altera¸c oes no espectro de energia. No entanto, as propriedades de transi¸c ao de fase SF-MI passam por mudan¸cas significativas devido ao efeito tipo Kerr. Outra caracter´ıstica importante que foi observada ´e que o efeito tipo Kerr favorece a fase MI.

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