Strongly interacting one-dimensional Bose condensates

Recent observation of Bose-Einstein condensation in dilute alkali gzises led to a great interest in this area both experimentally and theoretically. The most important characteristics of a Bose-Einstein condensate is that it consists of a large number of atoms occupying a single quantum state. This kind of a feature seen in photons led to the production of widely-used photon lasers. Coherent state of atoms may lead to the production of atom lasers in near future. The well-known Bogoliubov model to explain the nature of Bose-Einstein condensates of trapped dilute gases is valid when the interaction between particles is weak. However, as the number of atoms is increased, the interaction effects lead to a significant contribution in the system. Several attempts were made to improve the Bogoliubov model and to explain strongly interacting systems but these treatments are accurate up to a finite strength of the coupling . One-dimensional Bose systems is important because exact solution of the homogenous problem exists. Also it is a good testing ground to study interaction effects since only two-body interactions play role in these systems. Furthermore, experimental realization of one-dimensional systems are attracting a great deal of interest into the present problem. We investigate a somewhat different method to study the properties of strongly coupled Bose condensates in one-dimensional space. It uses the socalled Kohn-Sham theory to solve the problem by considering the exact solution of the homogenous one-dimensional Bose gas. The new approach reveals that interactions are expressed by a ■0^ term in the strongly coupled regime in contrast to a 0^ term in weak coupling regime. The model is applied to several types of trap potentials by performing a numerical minimization. We also improve the model for the case of a finite temperature. We observe that the system has a non-zero critical temperature which suggests a real phase transition in onedimensional space. In the last part, we work on the stability of a two-component condensate in a harmonic trap potential. We find that for a wide range of system parameters either a coexisting or a phase-segregated mixture can be obtained.