# One-dimensional sawtooth and zigzag lattices for ultracold atoms

## TL;DR

This paper introduces tunable optical lattices for ultracold atoms that can switch between zigzag and sawtooth shapes, enabling the study of quantum many-body states.

## Contribution

The paper presents a new method to control and tune lattice geometries for ultracold atoms, enabling nearly flat bands in sawtooth configurations.

## Key findings

- Zigzag and sawtooth lattices can be experimentally realized using superlattices with commensurate wavelengths.
- A nearly flat band is achievable in sawtooth lattices by tuning parameters, with the excited band's bandwidth reduced to 2% of the ground band.
- The proposed lattices offer a versatile platform for studying interaction-driven quantum states with ultracold atoms.

## Abstract

We describe tunable optical sawtooth and zigzag lattices for ultracold atoms. Making use of the superlattice generated by commensurate wavelengths of light beams, tunable geometries including zigzag and sawtooth configurations can be realised. We provide an experimentally feasible method to fully control inter- (t) and intra- (t′) unit-cell tunnelling in zigzag and sawtooth lattices. We analyse the conversion of the lattice geometry from zigzag to sawtooth, and show that a nearly flat band is attainable in the sawtooth configuration by means of tuning the lattice parameters. The bandwidth of the first excited band can be reduced up to 2% of the ground bandwidth for a wide range of lattice setting. A nearly flat band available in a tunable sawtooth lattice would offer a versatile platform for the study of interaction-driven quantum many-body states with ultracold atoms.