Preparation of edge states by shaking boundaries

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$\acute{\text{e}}$-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.

11 pages, 11 figures

References in corpus (6)

• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Long-distance entanglement and quantum teleportation in XX spin chains
• Entanglement generation between distant atoms by Lyapunov control
• Topological transitions of interacting bosons in one-dimensional bi-chromatic optical lattices
• Designing Topological Bands in Reciprocal Space