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

TL;DR

This paper investigates quantum bright solitons in an inhomogeneous Bose-Hubbard model with site-dependent interactions, revealing quantum effects like residual background density and the transition to Mott insulator phases.

Contribution

It demonstrates that quantum many-body effects allow soliton-like states with residual background density, differing from mean-field predictions, and explores the impact of strong interactions on these states.

Findings

Quantum solitons exhibit residual background density unlike mean-field solutions.

Self-trapping occurs for ter nd remains weakly localized below or certain interactions.

Strong onsite repulsion leads to Mott insulator phase with uniform density.

Abstract

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