Preparation of edge states by shaking boundaries

TL;DR

This paper proposes a boundary shaking method using Lyapunov control to prepare topological edge states in the Aubry-Andre9-Harper model, enabling state preparation from arbitrary initial conditions with boundary-only perturbations.

Contribution

It introduces a novel boundary shaking technique with Lyapunov control to efficiently generate edge states in the AAH model, including topological entangled states.

Findings

Edge states can be prepared from arbitrary initial states.

Control process depends on system size.

Boundary shaking effectively induces topological states.

Abstract

Preparing topological states of quantum matter, such as edge states, is one of the most important directions in condensed matter physics. In this work, we present a proposal to prepare edge states in Aubry-Andr$\acute{\textrm{e}}$-Harper (AAH) model with open boundaries, which takes advantage of Lyapunov control to design operations. We show that edge states can be obtained with almost arbitrary initial states. A numerical optimalization for the control is performed and the dependence of control process on the system size is discussed. The merit of this proposal is that the shaking exerts only on the boundaries of the model. As a by-product, a topological entangled state is achieved by elaborately designing the shaking scheme.