Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions

TL;DR

This study explores how the range of interparticle interactions influences the fragmentation of bosonic systems in different dimensions, revealing that long-range interactions increase fragmentation dependence on density and that fragmentation decreases with particle number.

Contribution

It provides a comprehensive analysis of the impact of interaction range on bosonic fragmentation across dimensions using a full many-body approach, highlighting new density and dimensional effects.

Findings

Fragmentation is density independent in 2D for contact interactions.

Long-range interactions increase fragmentation dependence on density.

Fragmentation decreases approximately as N^{-1/2} with particle number.

Abstract

The occupation of more than one single-particle state and hence the emergence of fragmentation is a many-body phenomenon universal to systems of spatially confined interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems. We solve the full many-body Schr\"odinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density and interaction strength is assessed. It is found that for contact interactions, the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long-ranged the interactions become. The degree of fragmentation is increasing, keeping the particle number $N$ fixed, when the density is decreasing as expected in one spatial dimension. We demonstrate that this remains, nontrivially, true also for long-range interactions in two spatial dimensions. We, finally, find that within our fully self-consistent approach, the fragmentation degree, to a good approximation, decreases universally as $N^{-1/2}$ when only $N$ is varied.