New gap states of matter waves in optical lattices

In this work we propose a completely new type of gap state corresponding to a finite extent nonlinear Bloch wave, in a condensate with repulsive particle interactions, which at a sufficient density is detuned into the linear band-gap. This localized state may therefore be of any width and consequently contain any number of particles. As these states correspond to the fundamental Bloch wave they are remarkably robust, and indeed in numerical simulations we have seen no evidence of instability for even the multi-vortex state. It is concluded that if the lattice is introduced non-adiabatically a condensate beginning in a harmonic trap may be easily localized in the lattice