Fibonacci optical lattices for tunable quantum quasicrystals

TL;DR

This paper introduces a novel quasiperiodic optical lattice based on Fibonacci tiling, enabling the simulation of quasicrystals with controllable properties for ultracold atoms, revealing multifractal spectra and edge states.

Contribution

It presents a physical realization of a Fibonacci-based quasicrystalline potential for ultracold atoms, enabling new quantum simulation experiments.

Findings

Multifractal energy spectrum observed

Singular continuous momentum-space structure identified

Controllable edge states demonstrated

Abstract

We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of the energies and wavefunctions of ultracold atoms loaded into such a lattice demonstrate a multifractal energy spectrum, a singular continuous momentum-space structure, and the existence of controllable edge states. These results open the door to cold atom quantum simulation experiments in tunable or dynamic quasicrystalline potentials, including topological pumping of edge states and phasonic spectroscopy.