A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions
Abstract
We show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van-der-Waals potentials and near Fano-Feshbach resonances. For van-der-Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pair-wise interaction can only be turned off for species with a small negative scattering length, leaving the Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.
Keywords
Cite
@article{arxiv.1604.01289,
title = {A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions},
author = {Saurabh Paul and P. R. Johnson and Eite Tiesinga},
journal= {arXiv preprint arXiv:1604.01289},
year = {2016}
}