Mechanisms of localization in a finite harmonically confined optical superlattice

TL;DR

This paper explores how harmonic confinement influences localization in finite optical superlattices, revealing different mechanisms and the role of topology, with implications for experimental observation and control.

Contribution

It identifies and analyzes distinct localization mechanisms in optical superlattices under harmonic confinement, emphasizing the role of topology and intermediate trapping frequencies.

Findings

Four lowest eigenstates form an effective four-level system in topologically non-trivial regimes

Larger trapping frequencies lead to classical localization similar to standard optical lattices

Topological edge states are affected by the harmonic trapping regime

Abstract

We investigate the impact of harmonic confinement in a finite optical superlattice and reveal the different mechanisms that can lead to the emergence of localized states. The optical superlattice, with odd or even number of unit cells, can exhibit either a trivial or a non-trivial underlying topology, characterized by the corresponding Zak phase. We focus on a distinct localization mechanism in the intermediate harmonic trapping frequency regime. Specifically, the four lowest-lying eigenstates in this regime form an effective four-level system in the topologically non-trivial configuration. Larger trapping frequency values drive the system into a harmonic trap dominated regime, featuring classical pairing and localization of all states of the lower band, as in a usual optical lattice. For the lower trapping frequency regime, the fate of topological edge states is discussed. Our results are based on exact diagonalization and on a tight-binding approximation that maps the continuous to a discrete system. We address several aspects relevant to the experimental implementation of optical superlattices and provide a brief illustration of the dynamics, highlighting direct ways to observe and distinguish between the different localization mechanisms.