# Archive ouverte HAL – Few-body bound states of two-dimensional bosons

### G. Guijarro 1 G. E. Astrakharchik 1 J. Boronat 1 B. BazakD. S. Petrov 2

#### G. Guijarro, G. E. Astrakharchik, J. Boronat, B. Bazak, D. S. Petrov. Few-body bound states of two-dimensional bosons. Physical Review A, American Physical Society 2020, ⟨10.1103/PhysRevA.101.041602⟩. ⟨hal-02537195⟩

We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a two-dimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atom-dimer interaction switches to repulsion.

• 1. UPC - Universitat Politècnica de Catalunya [Barcelona]
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques