Few-body bound states of two-dimensional bosons

Abstract

We study clusters of the type AN BM with N ≤ M ≤ 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 aAB and aAA = aBB, for sufficiently large attraction-to-repulsion ratios aAB/aBB. When aAB/aBB decreases below ≈ 10, the dimer-dimer interaction changes from attractive to repulsive and the populationbalanced 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 aAB ≈ 2aBB where the atom-dimer interaction switches to repulsion.

Ultradilute Quantum Liquid of Dipolar Atoms in a Bilayer

“…A possible underlying microscopic mechanism for the stabilization of the liquid is due effective three-dimer repulsion which balances an effective dimer-dimer attraction as proposed in Ref. [12]. Indeed, the three-dimer repulsive contribution is negligible for small densities and we find an energy which closely follows that of an attractive gas of dimers, shown by a dashed line in Fig.…”

“…1a. We found that the interlayer critical value for the liquid to gas transition (h/r 0 ≈ 1.1) is the same as the threshold value for the four-body bound state of dipolar bosons, when the tetramer breaks into two dimers [12].…”

“…The attractive part of the interlayer interaction potential, when strong enough, is sufficient to induce a phase transition from atomic to pair superfluids [10,11]. Recently, it has been predicted that addition of a three-dimer repulsion to a two-dimer attraction could stabilize a many-body liquid [12]. It is therefore an open challenge to determine the existence, formation mechanism, and properties of the self-bound many-body dipolar system in the bilayer geometry.…”

“…The best agreement is found for the smallest equilibrium and spinodal densities, i.e., for the largest h, for which the dipolar potential is well approximated by a contact potential with the same s-wave scattering length. The gaseous and selfbound phases are separated by the threshold h/r 0 ≈ 1.1 at which the effective dimer-dimer interaction changes its sign [12] from repulsion (gas) to attraction (homogeneous liquid or droplets). The gaseous regime features a second-order phase transition between atomic and molecular gas phases which on a qualitative level occurs when the molecular binding energy approaches the chemical potential.…”

Kinetic formation of trimers in a spinless fermionic chain

“…With the versatility of cold-atom platforms in terms of internal degrees of freedom and interactions, many proposals for trimers formation arose in the quantum matter literature, using spin balanced [12][13][14][15][16][17][18][19][20] or spinimbalanced fermionic mixtures [21][22][23], or fermions with different masses [24][25][26]. Signatures of bosonic trimers have also been discussed both in one [27][28][29][30] and two dimensions [31][32][33].…”