Large effective three-body interaction in a double-well optical lattice
Eite Tiesinga, Saurabh Paul
We study ultracold atoms in a double-well (DW) optical lattice and show that the low energy states of a multi-band Bose-Hubbard (BH) Hamiltonian with only pai r-wise interactions is equivalent to an effective single-band Hamiltonian with s trong three-body interactions. Each unit cell of the DW lattice has a symmetric double-well geometry along the $x$ axis and single well structure along the perp endicular directions. We obtain tunneling and two-body interaction energies from an exact band-structure calculation and numerically-constructed Wannier functions in order to construct a two-band BH Hamiltonian spanning the lowest two bands along the x axis and the ground band along the perpendicular directions. Our effective Hamiltonian is constructed from the ground state of the N-atom on-si te Hamiltonian for each unit cell obtained within the subspace spanned by the co rresponding Wannier functions. The model includes hopping between ground states in 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.
ultra-cold atoms, Hubbard models, optical lattice, effective three-bo dy interactions
and Paul, S.
Large effective three-body interaction in a double-well optical lattice, Physical Review A, [online], https://doi.org/10.1103/PhysRevA.92.023602
(Accessed November 29, 2023)