Preparation of topological modes by Lyapunov control

TL;DR

This paper proposes a Lyapunov control method to steer quantum systems into topological modes, such as Majorana zero modes and edge states, by manipulating boundary site parameters, with analysis of robustness and experimental feasibility.

Contribution

It introduces a novel Lyapunov control approach for preparing topological modes in quantum systems, applicable to both Fermi and Bose models, with practical considerations.

Findings

Successful steering of modes into Majorana zero modes and edge states.

Analysis of control fidelity sensitivity to perturbations.

Discussion on experimental implementation and pulse control.

Abstract

By Lyapunov control, we present a proposal to drive quasi-particles into a topological mode in quantum systems described by a quadratic Hamiltonian. The merit of this control is the individual manipulations on the boundary sites. We take the Kitaev's chain as an illustration for Fermi systems and show that an arbitrary excitation mode can be steered into the Majorana zero mode by manipulating the chemical potential of the boundary sites. For Bose systems, taking the noninteracting Su-Schrieffer-Heeger (SSH) model as an example, we illustrate how to drive the system into the edge mode. The sensitivity of the fidelity to perturbations and uncertainties in the control fields and initial modes is also examined. The experimental feasibility of the proposal and the possibility to replace the continuous control field with square wave pulses is finally discussed.