Abstract
A two-component Bose-Einstein condensate (BEC) described by two coupled a three-dimension Gross-Pitaevskii (GP) equations is considered, where one equation has dipole-dipole interaction while the other one has only the usual s-wave contact interaction, in a cigar trap. The time-splitting and sine spectral method in space is proposed to discretize the time-dependent equations for computing the dynamics of dipolar BEC. The singularity in the dipole-dipole interaction brings significant difficulties both in mathematical analysis and in numerical simulations. Numerical results are given to show the efficiency of this method.
Highlights
The achievement of the Bose-Einstein condensation of dilute gases in 1995 marked the beginning of a new era in atomic, molecular, and optical physics
In the last several years, there has been an investigation for realizing a new kind of quantum gases with the dipolar interaction, acting between particles having a permanent magnetic or electric dipole moment
The studies of the binary condensates were limited to the case of s-wave interaction, while a great deal of attention has been drawn recently to the dipolar Bose-Einstein condensate (BEC)
Summary
The achievement of the Bose-Einstein condensation of dilute gases in 1995 marked the beginning of a new era in atomic, molecular, and optical physics. The experimental realization of a BEC of 52Cr atoms [2, 3] at the University of Stuttgart in 2005 gave new impetus to the theoretical and the numerical investigations on these novel dipolar quantum gases at low temperature. More detailed and controlled experimental results have been obtained, illustrating the effects of phase separation in a multicomponent BEC [4,5,6]. In these papers, the studies of the binary condensates were limited to the case of s-wave interaction, while a great deal of attention has been drawn recently to the dipolar BEC
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