Three-body models in one dimension

Alexandre M. Zagoskin

Elmar Haller, Mohamed Rabie, Manfred J. Mark +5 more

We investigate local three-body correlations for bosonic particles in three dimensions and one dimension as a function of the interaction strength. The three-body correlation function g(3) is determined by measuring the three-body recombination rate in an ultracold gas of Cs atoms. In three dimensions, we measure the dependence of g(3) on the gas parameter in a BEC, finding good agreement with the theoretical prediction accounting for beyond-mean-field effects. In one dimension, we observe a reduction of g(3) by several orders of magnitude upon increasing interactions from the weakly interacting BEC to the strongly interacting Tonks-Girardeau regime, in good agreement with predictions from the Lieb-Liniger model for all strengths of interaction.

Simon Kreuzer, H.‐W. Hammer

Ludovic Pricoupenko

Following a strong analogy with two-dimensional physics, the three-body pseudopotential in one dimension is derived. The Born approximation is then considered in the context of ultracold atoms in a linear harmonic waveguide. The equivalence between this model and the three-body wave equation obtained directly from the Schr\"odinger equation, including the confinement potential of the waveguide, is demonstrated in the vicinity of the dimer threshold.

Mathieu Beau, Adolfo del Campo

We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to an arbitrary spatial dimension. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions.

Nouredine Zettili, ABDELKRIM BOUKAHIL