A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions

TL;DR

This paper derives a Hubbard model for ultracold bosonic atoms in optical lattices emphasizing dominant three-body interactions induced by zero-point energy effects, with potential for experimental realization.

Contribution

It introduces a Hubbard model with significant three-body interactions by controlling two-body interactions via Feshbach resonances and zero-point energy effects.

Findings

Three-body interactions can dominate in ultracold bosonic systems.

Conditions for tuning two-body interactions to near zero are identified.

Comparison of three-body interaction strength with hopping rates and recombination limits.

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 $^{88}$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.