Effective orbital ordering in multiwell optical lattices with fermionic atoms

TL;DR

This paper explores how fermionic atoms in optical superlattices can simulate complex spin-orbital interactions, revealing ground state patterns and the influence of hopping phases, thus advancing quantum simulation of correlated electron systems.

Contribution

It introduces a mapping between fermion ordering in optical lattices and spin-orbital models, specifically modifying the Kugel-Khomskii Hamiltonian for this context.

Findings

Ground states correspond to specific spin-pseudospin arrangements.

Fermion configurations depend on complex hopping phase patterns.

The model provides insights into quantum simulation of correlated materials.

Abstract

We consider the behavior of Fermi atoms on optical superlattices with two-well structure of each node. Fermions on such lattices serve as an analog simulator of Fermi type Hamiltonian. We derive a mapping between fermion quantum ordering in the optical superlattices and the spin-orbital physics developed for degenerate $d$-electron compounds. The appropriate effective spin-orbital model appears to be the modification of the Kugel-Khomskii Hamiltonian. We show how different ground states of this Hamiltonian correspond to particular spin-pseudospin arrangement patterns of fermions on the lattice. The dependence of fermion arrangement on phases of complex hopping amplitudes is illustrated.