Variation of the ground state properties of trapped Bose-Einstein condensate due to localized impurity

Abstract

Bose-Einstein condensates have been, by now, observed in as many as nine different atomic assemblies of bosons. Such a condensate is quantum mechanical interacting system whose ground state properties can be studied theoretically by solving the appropriate non-linear Gross-Pitaevskii-Ginzburg GPG equation. One can now study the change in the behavior of Bose-Einstein condensate by introducing a localized impurity which interacts with the condensate as a function of position of impurity in the condensate. The introduction of such an impurity can be mimicked by simply allowing an intensely focused laser beam to interact with the condensate. This would lead to alteration of ground state properties of the condensate as it would now interact with a potential of type <i>V Sech</i>²(r/w) where, <i>V</i> and <i>w</i> are amplitude and width of the impurity potential, respectively. The modified GPG equation in the presence of localized impurity potential as function of position in the condensate, has been numerically solved to obtain its various ground state properties as function of position, such as total energy per particle, chemical potential, kinetic, harmonic trap potential and two-body interaction energies per particle in addition to energy associated with impurity potential, correlation length, healing length etc. We have studied the behavior of the above-mentioned ground state properties as the position of localized impurity is changed in the condensate from core to peripheral position. While the total, harmonic oscillator potential and impurity energies decrease as the position of localized impurity is displaced from core of the condensate to its periphery, the value of two-body inter-particle interaction energy increases. Further, the values of chemical potential and total energy per particle shows decrease by ~ 9% and ~ 17% respectively, leading to the inference that the stability of condensate increases as the localized impurity is moved away from the core of the condensate.