Wannier-Stark states in double-periodic lattices I: one-dimensional lattices

TL;DR

This paper investigates the Wannier-Stark spectrum in one-dimensional double-periodic lattices, revealing how it transitions from two ladders to a single ladder as the static field strength increases, with analytical descriptions provided.

Contribution

It introduces an analytical framework for understanding the spectrum rearrangement in double-periodic lattices under varying static fields.

Findings

Spectrum is a superposition of two ladders at weak fields.

Spectrum reorganizes into a single ladder at strong fields.

Analytical expressions describe the spectrum transition.

Abstract

We analyze the Wannier-Stark spectrum of a quantum particle in generic one-dimensional double-periodic lattices. In the limit of weak static field the spectrum is shown to be a superposition of two Wannier-Stark ladders originated from two Bloch subbands. As the strength of the field is increased, the spectrum rearranges itself into a single Wannier-Stark ladder. We derive analytical expressions which describe the rearrangement employing the analogy between the Wannier-Stark problem and the driven two-level system in the strong-coupling regime.