Universal dimerized quantum droplets in a one-dimensional lattice

TL;DR

This paper investigates the formation and properties of quantum droplets in a one-dimensional lattice of two-component bosons, revealing a universal behavior governed by dimer interactions and demonstrating fermionization and soliton formation.

Contribution

It introduces an effective dimer model that accurately describes quantum droplets in 1D lattices, validated against exact DMRG results, and uncovers universal dimer-dimer interaction effects.

Findings

Quantum droplets form due to finite-range dimer interactions.

Dimer-dimer scattering length and effective range determine droplet stability.

Fermionization occurs at strong dimer-dimer repulsion, leading to Tonks-Girardeau states.

Abstract

The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive inter-component and repulsive intra-component interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by DMRG method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state. Finally, we identify conditions for the formation of a solitonic solution.