Landau-Zener-St\"uckelberg interference in edge state pumping

TL;DR

This paper reveals that adiabatic edge state pumping involves Landau-Zener-Stückelberg interference, with non-adiabatic points affecting the process, especially in disordered systems, providing new insights into topological quantum dynamics.

Contribution

It uncovers the non-adiabatic physics underlying edge state pumping, linking it to LZS interference and explaining the breakdown in disordered chains.

Findings

Edge state pumping involves two non-adiabatic points.

LZS interference determines the edge state's fate.

Weak disorder can cause breakdown of pumping due to anti-crossings.

Abstract

The adiabatic edge state pumping (ESP) in one dimensional model, which has important applications in topological phase transition and quantum simulation, has been widely performed in both theories and experiments. This phenomenon has been observed in some systems with sizes $L = 9 - 100$, and it seems that due to the topological protection, the ESP can be survived even in the presence of weak random potential. Yet the fundamental issues of adiabaticity for this process have not been clarified. In this paper, we revisit this problem and show that this process involves two non-adiabatic points during the transition between the edge state and bulk state, yielding non-abadiatic physics. As a result, the ESP can be described by the Landau-Zener-St\"{u}ckelberg (LZS) interference process, in which the relative phase between the edge state and the bulk state determine the fate of the edge state during pumping. Furthermore, in a relatively long chain with weak disorder, the ESP can break down due to the anti-crossing of the edge state and the bulk edge states. We unveil these physics in terms of non-adiabaticity. The new mechanisms for ESP unveiled in this work is readily accessible in experiment, and shall therefore offer a down-to-earth platform for the intriguing LZS dynamics in terms of edge states.