Numerical Solution of the Gross-Pitaevskii Equation in Cylindrical Coordinates

Josh Soneson

Program in Applied Mathematics
University of Arizona

I will present a numerical method introduced in S.K. Adhikari: cond-math/0005450 (2000) for solving the two-dimensional time-independent Gross-Pitaevskii equation (GPE) in cylindrical coordinates. Recently a modified version of this method was used to determine the steady-state wavefunction of a Bose-Einstein condensate with repulsive many-body interactions in an optical dipole trap based on a Bessel light beam. This in part shows that the first-order Bessel beams are able to produce tightly confined atomic waveguides. Future studies will also be discussed, including the use of Bessel beam traps as atom funnels and velocity filters.