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

Abstract

The stability of an attractive Bose–Einstein condensate on a joint one-dimensionaloptical lattice and an axially symmetrical harmonic trap is studied using thenumerical solution of the time-dependent mean-field Gross–Pitaevskii equationand the critical number of atoms for a stable condensate is calculated. We alsocalculate this critical number of atoms in a double-well potential which isalways greater than that in an axially symmetrical harmonic trap. Thecritical number of atoms in an optical trap can be made smaller or largerthan the corresponding number in the absence of the optical trap bymoving a node of the optical lattice potential in the axial direction of theharmonic trap. This variation of the critical number of atoms can beobserved experimentally and compared with the present calculations.