A two-parameter continuation algorithm for vortex pinning in rotating Bose-Einstein condensates

We describe an efficient two-parameter continuation algorithm combined with spectral collocation methods for computing the ground state and central vortex state solutions of rotating Bose-Einstein condensates in optical lattices, where the first kind and second kind Chebyshev polynomials are used as the basis functions for the trial function space. By treating the chemical potential and angular velocity as the continuation parameters simultaneously under the additional constraint of normalization condition, the proposed algorithm can effectively compute numerical solutions for a rich variety of physical phenomena observed in physical experiments with very little cost. Comparisons with various numerical methods on some sample test problems are reported.