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We study the winding number dependence of the stationary states of aBose-Einstein condensate in a ring-shaped lattice. The system is obtained byconfining atoms in a toroidal trap with equally spaced radial barriers. Wecalculate the energy and angular momentum as functions of the winding numberand the barrier height for two quite distinct particle numbers. In both caseswe observe two clearly differentiated regimes. For low barriers, metastablevortex states are obtained up to a maximum winding number which depends on theparticle number and barrier height. In this regime, the angular momentum andenergy show, respectively, almost linear and quadratic dependences on thewinding number. For large barrier heights, on the other hand, stationary statesare obtained up to a maximum winding number which depends only on the number oflattice sites, whereas energy and angular momentum are shown to be sinusoidalfunctions of the winding number.

Winding number dependence of Bose-Einstein condensates in a ring-shaped lattice