Structure-dynamics relation in shaken optical lattices

TL;DR

This paper establishes a general relation between the geometry of shaken optical lattices and their effective tunneling dynamics, providing a framework to derive effective Hamiltonians for various lattice geometries.

Contribution

It introduces a universal relation linking lattice geometry to effective tunneling, enabling straightforward derivation of Hamiltonians in shaken optical lattices.

Findings

Identifies symmetry properties of tunneling rates in different lattice geometries.

Provides a method to derive truncated effective Hamiltonians.

Illustrates the relation with three example lattices.

Abstract

Shaken optical lattices permit to coherently modify the tunneling of particles in a controllable manner. We introduce a general relation between the geometry of shaken lattices and their admissible effective dynamics. Using three different examples, we illustrate the symmetries of the emerging tunneling rates. The results provide a clear framework to understand the relation between lattice geometry and accessible dynamics, and a tool to straightforwardly derive truncated effective Hamiltonians on arbitrary geometries.