One-dimensional three-boson problem with two- and three-body interactions

Abstract

We solve the three-boson problem with contact two-and three-body interactions in one dimension and analytically calculate the ground and excited trimer-state energies. Then, by using the diffusion Monte Carlo technique we calculate the binding energy of three dimers formed in a one-dimensional Bose-Bose or Fermi-Bose mixture with attractive interspecies and repulsive intraspecies interactions. Combining these results with our three-body analytics, we extract the three-dimer scattering length close to the dimer-dimer zero crossing. In both considered cases the three-dimer interaction turns out to be repulsive. Our results constitute a concrete proposal for obtaining a one-dimensional gas with a pure three-body repulsion.PACS numbers:

Beyond Lee-Huang-Yang description of self-bound Bose mixtures

“…In other words, the instability is predicted in the regime where the Bogoliubov theory is not applicable. It has been found in QMC simulations [15] that the liquid evaporates for δg/g > 0.54, in agreement with threshold value where effective interaction between dimers becomes attractive [37] while three-dimer interaction is still repulsive [38].…”

Three-body interaction near a narrow two-body zero crossing

“…In particular, three-body forces have been considered in the context of droplet formation in three dimensions [16][17][18][19] and as a means for stabilizing supersolid phases of quasi-two-dimensional dipolar atoms or molecules [20]. Quite a few recent theory papers have discussed one-dimensional three-bodyinteracting systems, exploring the kinematic equivalence of the three-body scattering in one dimension and the two-body scattering in two dimensions (see, for example [21][22][23][24][25][26][27][28][29][30][31][32]).…”

Direct Measurements of Collisional Dynamics in Cold Atom Triads

“…Three-body recombination occurs throughout physics from ultracold plasmas [33] to chemistry [34] and astrophysics [35] and has been extensively studied in ultracold atoms [22,[36][37][38][39][40][41]. Moreover, the rich physics of idealised three atom systems in tightly confining traps is currently the target of intensive theoretical studies [42][43][44][45][46][47], while experiments are presently lacking.…”