Quantum bright solitons in the Bose-Hubbard model with site-dependent repulsive interactions

We introduce a one-dimensional spatially inhomogeneous Bose-Hubbard model (BHM) with the strength of the onsite repulsive interactions growing, with the discrete coordinate zj, as |zj|α with α>0. Recently, the analysis of the mean-field (MF) counterpart of this system has demonstrated self-trapping of robust unstaggered discrete solitons, under the condition α>1. By using the numerically implemented method of the density matrix renormalization group, we demonstrate that, in a certain range of the interaction, the BHM also features self-trapping of the ground state into a soliton-like configuration, at α>1, and remains weakly localized at α<1. An essential quantum feature found in the BHM is a residual quasi-constant density of the background surrounding the soliton-like peak in the ground state, while in the MF limit the finite-density background is absent. Very strong onsite repulsion eventually destroys soliton-like states, driving the system, at integer densities, into the Mott phase with a spatially uniform density.