Quantum signatures of self-trapping transition in attractive lattice bosons

TL;DR

This paper investigates the quantum signatures of the self-trapping transition in attractive lattice bosons by comparing quantum ground states with semiclassical predictions, revealing localization and bifurcation patterns at finite particle numbers.

Contribution

It demonstrates how quantum properties reflect semiclassical self-trapping phenomena, highlighting finite-number effects in the Bose-Hubbard model.

Findings

Quantum ground states show localization consistent with semiclassical self-trapping.

Bifurcation patterns in the semiclassical theory are observable in quantum properties.

Finite particle number influences the quantum signatures of the transition.

Abstract

We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice, and compare the relevant ground-state properties with those of the corresponding symmetry-breaking semiclassical nonlinear theory. The introduction of a suitable measure allows us to highlight many correspondences between the nonlinear theory and the inherently linear quantum theory, characterized by the well-known self-trapping phenomenon. In particular we demonstrate that the localization properties and bifurcation pattern of the semiclassical ground-state can be clearly recognized at the quantum level. Our analysis highlights a finite-number effect.