Preparation of topological modes by Lyapunov control.
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.
School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China.
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Shi
School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China.
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Zhao
Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China.
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Yi