Edge state preparation in one dimensional lattice by quantum Lyapunov control

Abstract

Quantum Lyapunov control uses a feedback control methodology to determine control fields which are applied to control quantum systems in an open-loop way. In this work, we adopt two Lyapunov control schemes to prepare an edge state for a fermionic chain consisted of cold atoms loaded in an optical lattice. Such a chain can be described by the Harper model. Corresponding to the two schemes, state distance and state error Lyapunov functions are considered. The results show that both the schemes are effective to prepare the edge state within a wide range of parameters. We found that the edge state can be prepared with high fidelity even \textbf{if} there are moderate fluctuations in on-site or hopping potentials. Both control schemes can be extended to similar chains (3$m+d$, $d$=2) of different lengths. Since regular amplitude control field is easier to apply in practice, amplitude-modulated control fields are used to replace the unmodulated one to prepare the edge state. Such control approaches provide tools to explore edge states for one dimensional topological materials.

References in corpus (5)

• One-dimensional Topological Edge States of Bismuth Bilayers
• Manipulating Topological Edge Spins in One-Dimensional Optical Lattice
• Interference pattern and visibility of a Mott insulator
• Effect of interactions on the localization of a Bose-Einstein condensate in a quasi-periodic lattice
• The edge engineering of topological Bi(111) bilayer