Edge Localized Schr\"odinger Cat States in Finite Lattices via Periodic Driving

TL;DR

This paper investigates how periodic driving in finite lattice systems creates edge Schrödinger cat states, resolving discrepancies between tight-binding and continuum models, and demonstrating state localization at edges under specific conditions.

Contribution

It introduces a unified explanation for edge states in driven finite lattices, revealing their cat-like nature and conditions for localization, bridging prior model discrepancies.

Findings

Edge bands are Schrödinger cat-like states with effective tunneling.

External driving induces collapse of bulk bands and localization of edge states.

Discrepancies between tight-binding and continuum models are resolved.

Abstract

Floquet states have been used to describe the impact of periodic driving on lattice systems, either using a tight-binding model, or by using a continuum model where a Kronig-Penney-like description has been used to model spatially periodic systems in one dimension. A number of these studies have focused on finite systems, and results from these studies are distinct from those of infinite lattice systems as a consequence of boundary effects. In the case of a finite system, there remains a discrepancy in the results between tight-binding descriptions and continuous lattice models. Periodic driving by a time-dependent field in tight-binding models results in a collapse of all quasienergies within a band at special driving amplitudes. In the continuum model, on the other hand, a pair of nearly-degenerate edge bands emerge and remain gapped from the bulk bands as the field amplitude increases. We resolve these discrepancies and explain how these edge bands represent Schr\"odinger cat-like states with effective tunneling across the entire lattice. Moreover, we show that these extended cat-like states become perfectly localized at the edge sites when the external driving amplitude induces a collapse of the bulk bands.