Dipolar bose-einstein condensate in a cylindrically symmetric trap
Bose-Einstein Condensate (BEC) and particularly its stability dynamics has been a subject to many investigations since the first realization of this new condensed state in alkali atoms interacting via short range potential. Short range or contact interactions account for a great number of physical properties ranging from formation of quantum vortices to the super uid character of cold gases. In this thesis, dipolar Bose-Einstein condensate, which inherently possess longrange and anisotropic potential for the interaction of the constituent particles, is studied and its stability depending on the geometry of the system is investigated. The dipolar Bose gas is confined to a cylindrically symmetric harmonic trap and the dipoles within the gas is initially oriented along the symmetry axis of the confining prolate trap. In the condensed state, the condensate is observed to be elongated along harmonic trap symmetry axis as long as the axis corresponds to weak confinement direction. This elongation is understood to be resulting from the energy minimization of the system by adding the dipoles head to tail along the center of the trap, thereby determining the nature of the long-range interaction to be attractive and the condensate is liable to collapse. Below a certain value for the ratio of the dipolar and contact interactions (Edd = Cdd=3g = 1), the condensate is stable, while above this value it undergoes collapse. In the opposite case where the trap axis is the strong confinement direction (oblate trap), the elongation occurs perpendicularly to the symmetry axis of the confining trap (with highly oblate geometry) with the energetically most favorable configuration being the alignment of the dipoles side by side implying mostly repulsive interactions in which case the condensate is always stable. To further understand the effect of the geometry on the stability, the dipoles are finally oriented at an angle from the trap axis by tuning the external field and elongation direction of the condensate is calculated; stable, metastable and unstable states of the condensate are observed in this new geometry.