Topology, edge states, and zero-energy states of ultracold atoms in 1D optical superlattices with alternating onsite potentials or hopping coefficients

TL;DR

This paper explores the topological and symmetry-related properties of one-dimensional ultracold atom superlattices with alternating potentials or hopping, highlighting localized and zero-energy states and their experimental detection.

Contribution

It provides a systematic study of topological invariants and zero-energy states in 1D optical superlattices, including feasible experimental realizations.

Findings

Superlattices exhibit quantized topological invariants in augmented parameter space.

Localized and zero-energy states are associated with Hamiltonian symmetries.

Proposed methods enable experimental probing of these states in ultracold atoms.

Abstract

One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices allow a systematic study of those properties in superlattices with or without boundaries. While superlattices with additional modulating parameters are shown to have quantized topological invariants in the augmented parameter space, we also found localized or zero-energy states associated with symmetries of the Hamiltonians. Probing those states in ultracold-atoms is possible by utilizing recently proposed methods analyzing particle depletion or the local density of states. Moreover, we summarize feasible realizations of configurable optical superlattices using currently available techniques.