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

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 interspecies 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 ground and excited state energies reported here are exact within the respective Hilbert spaces, which have been adapted according to a given set of single-particle basis states and a specific importance threshold of the employed truncation method. We compare these data to the usual ad hoc inclusion of higher-order contributions in the extended Gross-Pitaevskii equation. For the given parameters we find a remarkable agreement between the few-body regime and the thermodynamic limit in one dimension.