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.
Highlights
By Lyapunov control, we present a proposal to drive quasi-particles into a topological mode in quantum systems described by a quadratic Hamiltonian
For a Fermi system described by the Kitaev model, we show how to steer an arbitrary initial mode into the Majorana zero mode by manipulating the chemical potential of the boundary sites
We show that the control field can be replaced with square wave pulses, which might make the realization of the control much easier in experiments
Summary
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. By the use of Lyapunov control technique, we present a method to manipulate the topological modes in both Fermi and Bose systems. For a Fermi system described by the Kitaev model, we show how to steer an arbitrary initial mode into the Majorana zero mode by manipulating the chemical potential of the boundary sites. We show that the control field can be replaced with square wave pulses, which might make the realization of the control much easier in experiments
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