Solitons in trapped Bose-Einstein condensates in one-dimensional optical lattices

We use quantum Monte Carlo simulations to show the presence and study the properties of solitons in the one-dimensional soft-core bosonic Hubbard model with near-neighbor interaction in traps. We show that when the half-filled charge density wave (CDW) phase is doped, solitons are produced and quasi-long-range order established. We discuss the implications of these results for the presence and robustness of this solitonic phase in Bose-Einstein condensates on one-dimensional optical lattices in traps and study the associated excitation spectrum. The density profile exhibits the coexistence of Mott insulator, CDW, and superfluid regions.