Homogeneous mixtures of bosonic atoms with Josephson coupling at a finite temperature

Author(s)

Marcelo Oliveira da Costa Pires

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2005-11-01

Examining board members

Emerson Jose Veloso de Passos; Frederico Firmo de Souza Cruz; Arnaldo Gammal; Antonio Fernando Ribeiro de Toledo Piza; Lauro Tomio

• Advisor: Emerson Jose Veloso de Passos

Abstract

We use the principle of maximum entropy to derive the Gross-Pitaevskii and the HartreeFock-Bogoliubov equations which describe the equilibrium states and the collective excitations of a binary homogeneous mixture of bosonic atoms in two different hyperfine states, in the presence of an internal Josephson coupling, at a finite temperature. To correct the absence of a gapless excitation branch in the Hartree-Fock-Bogolibov theory, we show how to extend the Popov approximation to the case of condensate mixtures. We calculate, as function of the temperature, physical quantities such as the fraction of atoms in the condensates, the spectra of collective excitations, the gap and the speed of sound. We investigate how the bistable structure found at null temperature changes when we increase the temperature, starting at T = O. When one heat the mixture, depending on the values of the system\'s parameters, we note that the bi-stability disappears at a temperature smaller than the transition temperature, either by the instability of one of the equilibrium states or by the degeneracy of the two stable equilibrium states. (AU)