Abstract

This talk tackles with the problem regarding a two-component Bose-Einstein Condensate with long-range anisotropic dipole-dipole interaction into consideration. With the method of Bogoliubov prescription of a gand-canonical Hamiltonian in second quantization form, the zeroth, first and second order terms are separated and discussed separately which all yield to different physical interpretations. Subsequently, by introducing a canonical transformation of the two component creation and annihilation operators, the matrix of fluctuation term is diagonalized which results in two branches of Bogoliubov spectrum. Further, the condensate depletion, ground-state energy shift, chemical potential and state of equation are calculated separately for homogeneous systems. When it comes to the harmonically-trapped systems, semi-classical approximation is used to deal with the spatial dependence. A similar form of Bogoliubov-de Gennes (BdG) equation is obtained under Thomas-Fermi regime where the kinetic energy of atoms can be neglected. Together with local density approximation, the non-local BdG is transmitted into an algebraic solvable equation. Later the Boboliubov amplitudes are solved in the same form as homogenous case only with the substitution of the non-local term.