Attractive ultracold bosons in a necklace optical potential

TL;DR

This paper investigates the ground state properties of attractive bosons in a one-dimensional necklace optical lattice, comparing quantum and semiclassical models, and finds that semiclassical equations accurately describe quantum states even in strongly interacting regimes.

Contribution

It introduces a modified semiclassical approach with a correction factor that accurately captures quantum ground states across weak to strong interactions in a necklace optical lattice.

Findings

Semiclassical equations match quantum ground states even at large interactions.

Quantum superpositions resemble localized symmetry-breaking states.

Three regimes identified based on hopping to interaction ratio.

Abstract

We study the ground state properties of the Bose-Hubbard model with attractive interactions on a M-site one-dimensional periodic -- necklace-like -- lattice, whose experimental realization in terms of ultracold atoms is promised by a recently proposed optical trapping scheme, as well as by the control over the atomic interactions and tunneling amplitudes granted by well-established optical techniques. We compare the properties of the quantum model to a semiclassical picture based on a number-conserving su(M) coherent state, which results into a set of modified discrete nonlinear Schroedinger equations. We show that, owing to the presence of a correction factor ensuing from number conservation, the ground-state solution to these equations provides a remarkably satisfactory description of its quantum counterpart not only -- as expected -- in the weak-interaction, superfluid regime, but even in the deeply quantum regime of large interactions and possibly small populations. In particular, we show that in this regime, the delocalized, Schroedinger-cat-like quantum ground state can be seen as a coherent quantum superposition of the localized, symmetry-breaking ground-state of the variational approach. We also show that, depending on the hopping to interaction ratio, three regimes can be recognized both in the semiclassical and quantum picture of the system.