Few-boson processes in the presence of an attractive impurity under one-dimensional confinement

Abstract

We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with δ functions, but due to the mass imbalance the problem is nonintegrable. Universal few-body binding energies, atom-dimer and atom-trimer scattering lengths, are all calculated in terms of two parameters, namely the mass ratio m L /m H , and ratio g HH /g HL of the δ-function couplings. We specifically identify the values of these ratios for which the atom-dimer or atom-trimer scattering lengths vanish or diverge. We identify regions in this parameter space in which various few-body inelastic processes become energetically allowed. In the Tonks-Girardeau limit (g HH → ∞), our results are relevant to experiments involving trapped fermions with an impurity atom.

Few strongly interacting ultracold fermions in one-dimensional traps of different shapes

“…Apart from a few exceptions [34][35][36][37][38][39][40][41], it has commonly been assumed that particles of different kinds have the same mass and the main impact on properties of the system comes from an imbalance of the number of particles. However, recently it was shown that for particles confined in a harmonic trap, the mass difference between different fermionic components leads to their spatial separation if interactions are strong enough [42].…”

Integrable Families of Hard-Core Particles with Unequal Masses in a One-Dimensional Harmonic Trap

“…The possibility for experimental implementation of mass-imbalanced atomic systems has driven multiple recent analyses. For general masses with contact interactions in an equal-frequency harmonic trap there are no exact solutions, so most previous approaches have relied on approximation schemes and numerical methods [25][26][27][28][29][30][31][32]. In this article, we show that for hard-core interactions there exist families of unequal masses for which there are exact solutions for the ground state and all excited states.…”

“…The domain is a simplex whose shape depends on the mass ratios. For three particles, the six ordering sectors are just arcs of a circles and every set of masses is therefore integrable arXiv:1704.01433v3 [quant-ph] 28 Aug 2017 by separation of variables. For four particles, the 24 ordering sectors are spherical triangles.…”

Complex collisions of ultracold molecules: A toy model

“…In addition to being difficult to experimentally measure, molecule-molecule collisions are extremely challenging to model, and quantitative calculations remain impossible for most diatomic molecules, including bialkali molecules. Recent work has emphasized the high resonance density inherent to bialkali (and heavier) atom-molecule [63][64][65][88][89][90][91][92][93] and molecule-molecule [94][95][96] collisions, building on earlier research on molecules formed from lighter atoms [61,[97][98][99][100][101][102][103][104][105].…”