Few-body bound states of bosonic mixtures in two-dimensional optical lattices

TL;DR

This paper investigates how bound states form in small two-dimensional optical lattices with bosonic mixtures, revealing unique non-monotonic binding energy behaviors not seen in one-dimensional systems.

Contribution

It provides the first comprehensive numerical analysis of few-body bosonic bound states in 2D optical lattices, highlighting differences from 1D systems.

Findings

Bound clusters of all bosons can form in 2D lattices.

Binding energy exhibits non-monotonic dependence on interspecies interaction.

Distinct binding mechanisms compared to 1D bosonic mixtures.

Abstract

We study the formation of bound states in a binary mixture of a few bosons in small square optical lattices. Using the exact diagonalization method, we find that bound clusters of all available bosons can form. We provide a comprehensive numerical examination of these bound states for a wide range of repulsive intraspecies and attractive interspecies interactions. In contrast to binary mixtures in one-dimensional chains, we reveal that the binding energy of the clusters shows a non-monotonic dependence on the interspecies interaction strengths for small tunneling rates, developing a local minimum for intermediate attractive interactions. The findings of this work highlight the difference between the binding mechanisms of binary bosonic mixtures in one- and higher-dimensional lattices.