The critical number of atoms in an attractive Bose–Einstein condensate on optical plus harmonic traps

The stability of an attractive Bose–Einstein condensate on a joint one-dimensional optical lattice and an axially symmetrical harmonic trap is studied using the numerical solution of the time-dependent mean-field Gross–Pitaevskii equation and the critical number of atoms for a stable condensate is calculated. We also calculate this critical number of atoms in a double-well potential which is always greater than that in an axially symmetrical harmonic trap. The critical number of atoms in an optical trap can be made smaller or larger than the corresponding number in the absence of the optical trap by moving a node of the optical lattice potential in the axial direction of the harmonic trap. This variation of the critical number of atoms can be observed experimentally and compared with the present calculations.