Ground Band and Excited Band of Spin-1 BEC in Cigar Shaped Laser Trap

The wavefunctions that conserve the total spin are constructed for the fully condensed states and the states with one particle excited. A set of equations are deduced for the spatial longitudinal wavefunctions and the chemical potentials. These equations are solved numerically for ²³Na and ⁸⁷Rb condensates. The deformed trap shows significant effects on the spectrum. This implies that the spin effect of the spinor BEC are more easily detected in an optical trap of larger aspect ratio.