Large effective three-body interaction in a double-well optical lattice

TL;DR

This paper demonstrates that ultracold atoms in a double-well optical lattice can be effectively described by a single-band Hamiltonian with strong, tunable three-body interactions, simplifying the analysis of complex many-body phenomena.

Contribution

The authors derive an effective single-band Hamiltonian with significant three-body interactions from a multi-band Bose-Hubbard model in a double-well optical lattice, validated by numerical simulations.

Findings

Effective Hamiltonian includes strong, tunable three-body interactions.

Numerical mean-field simulations show excellent approximation across phases.

Model applicable over a wide range of lattice parameters.

Abstract

We study ultracold atoms in an optical lattice with two local minima per unit cell and show that the low energy states of a multi-band Bose-Hubbard (BH) Hamiltonian with only pair-wise interactions is equivalent to an effective single-band Hamiltonian with strong three-body interactions. We focus on a double-well optical lattice with a symmetric double well along the $x$ axis and single well structure along the perpendicular directions. Tunneling and two-body interaction energies are obtained from an exact band-structure calculation and numerically-constructed Wannier functions in order to construct a BH Hamiltonian spanning the lowest two bands. Our effective Hamiltonian is constructed from the ground state of the $N$-atom Hamiltonian for each unit cell obtained within the subspace spanned by the Wannier functions of two lowest bands. The model includes hopping between ground states of neighboring unit cells. We show that such an effective Hamiltonian has strong three-body interactions that can be easily tuned by changing the lattice parameters. Finally, relying on numerical mean-field simulations, we show that the effective Hamiltonian is an excellent approximation of the two-band BH Hamiltonian over a wide range of lattice parameters, both in the superfluid and Mott insulator regions.