Superfluid-droplet crossover in a binary boson mixture on a ring: Exact diagonalization solutions for few-particle systems in one dimension

TL;DR

This paper uses exact diagonalization to study how quantum droplets form in a one-dimensional binary boson mixture, revealing how self-binding influences rotational excitations and comparing few-body results with mean-field theories.

Contribution

It provides the first exact diagonalization analysis of superfluid-droplet crossover in a 1D binary boson system, connecting few-body and many-body behaviors.

Findings

Formation of self-bound droplets at critical interactions

Transition from superfluid to rigid body rotational spectra

Good agreement between exact few-body results and extended Gross-Pitaevskii theory

Abstract

We investigate the formation of self-bound quantum droplets in a one-dimensional binary mixture of bosonic atoms, applying the method of numerical diagonalization of the full Hamiltonian. The excitation spectra and ground-state pair correlations signal the formation of a few-boson droplet when crossing the region of critical inter-species interactions. The self-binding affects the rotational excitations, displaying a change in the energy dispersion from negative curvature, associated with superfluidity in the many-body limit, to a nearly parabolic curvature indicative of rigid body rotation. We exploit two global symmetries of the system to further analyze the few-body modes in terms of transition matrix elements and breathing mode dynamics. The exact results are compared to the usual ad-hoc inclusion of higher-order contributions in the extended Gross-Pitaevskii equation, showing a remarkable agreement between the few-body regime and the thermodynamic limit in one dimension.