Edge states and topological phases in one-dimensional optical superlattices

TL;DR

This paper demonstrates that one-dimensional optical superlattices can host topological edge states and phases, typically associated with higher dimensions, revealed through density profiles and spectral features.

Contribution

It shows that 1D optical superlattices can exhibit topological phases and edge states, expanding the understanding of topological phenomena beyond 2D systems.

Findings

Edge states appear in 1D superlattices with nonzero topological invariants.

Density profiles display quantized plateaus related to lattice wavelength ratios.

Finite-temperature density profiles reveal the butterfly-like Hofstadter spectrum.

Abstract

We show that one-dimensional quasi-periodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on the optical superlattice is a topological insulator characterized by a nonzero topological invariant. The topological nature can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions uniquely determined by the ration of wavelengths of the bichromatic optical lattice. The butterfly-like spectrum of the superlattice system can be also determined from the finite-temperature density profiles of the trapped fermion system. This finding opens an alternative avenue to study the topological phases and Hofstadter-like spectrum in one-dimensional optical lattices.