Edge state preparation in one dimensional lattice by quantum Lyapunov control

TL;DR

This paper demonstrates effective methods using quantum Lyapunov control to prepare edge states in a one-dimensional fermionic chain modeled by the Harper model, with high fidelity even under potential fluctuations.

Contribution

It introduces two Lyapunov control schemes for edge state preparation in a fermionic chain, extending their applicability and using amplitude-modulated control fields for practical implementation.

Findings

Both control schemes effectively prepare edge states across various parameters.

High fidelity edge state preparation is robust against moderate potential fluctuations.

Control methods can be extended to chains of different lengths.

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.