Phase diagram and elementary excitations of strongly interacting droplets with non-local interactions

TL;DR

This paper investigates the properties of one-dimensional quantum droplets formed by strongly interacting bosons with non-local interactions, analyzing their structure, energies, and excitation spectra in the Tonks-Girardeau limit.

Contribution

It provides a unified analysis of droplet features across various non-local potentials and derives approximate formulas for energies in the slowly varying density regime.

Findings

Droplets exhibit flat-top density profiles in the Tonks-Girardeau limit.

Excitation spectrum includes phononic-like and scattering modes.

Surface and bulk energies are approximated for slowly varying densities.

Abstract

A one-dimensional bosonic gas with strong contact repulsion and attractive non-local interactions may form a quantum droplet with a flat-top density profile. We focus on a system in the Tonks-Girardeau limit of infinitely strong contact repulsion. We show that the main system features are the same for a broad class of non-local interaction potentials. Then, we focus on a limiting case, the one of slowly varying density profiles, to find approximate formulas for the surface and bulk energies of a droplet. We further characterise the system by numerically finding the excitation spectrum. It consists of two families: phononic-like excitations inside droplets and scattering modes. Analysis within the linearised regime is supplemented with the full, nonlinear dynamics of small perturbations.