Universal bound states of one-dimensional bosons with two- and three-body attractions

Abstract

When quantum particles are confined into lower dimensions, an effective three-body interaction inevitably arises and may cause significant consequences. Here we study bosons in one dimension with weak two-body and three-body interactions, predict the existence of two three-body bound states when both interactions are attractive, and determine their binding energies as universal functions of the two-body and three-body scattering lengths. We also show that an infinitesimal three-body attraction induces an excited bound state only for 3, 39, or more bosons. Our findings herein have direct relevance to a broad range of quasi-one-dimensional systems realized with ultracold atoms.

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

“…Then, the dimer states given by Eqs. (23)(24)(25) are spurious, consistent with the fact that the zero-range theory can no longer be used at such high momenta.…”

“…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

“…This could happen due to the strong confinement by the tweezer or the presence of the intense tweezer light. Finally, strong transverse confinement affects the Efimov physics of three-body bound states [43] and resonances, and it is presently unknown where these reside for our trap geometry. While the presence of an Efimov resonance would likely rather enhance the threebody loss rate compared to the background, it is also possible that destructive interference between resonant and non-resonant scattering (Fano effect) could reduce the loss rate, as was observed in Ref.…”

“…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.…”

Universality in a one-dimensional three-body system

“…Many theoretical studies [18,19,[34][35][36] of three-body systems confined along two directions are performed using 1D models. This reduction offers the advantage of a simple and intuitive description revealing the underlying three-body properties.…”