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Preparation of topological modes by Lyapunov control.

Shi ZC, Zhao XL, Yi XX - Sci Rep (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China.

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.

No MeSH data available.


The energy spectrum and spatial distributions of the BdG Hamiltonian  describing the Kitaev’s chain with total number N = 30 of sites. We have set the lattice spacing as units. There exists two Majorana modes in the band gap, i.e., the 30th and 31th eigenmodes. The 30th eigenmode is labeled by left mode and the 31th is labeled by right mode. (b,c) are the coefficients X30 and Y30 of the left mode, while (d,e) are the coefficients X31 and Y31 of the right mode.
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f1: The energy spectrum and spatial distributions of the BdG Hamiltonian describing the Kitaev’s chain with total number N = 30 of sites. We have set the lattice spacing as units. There exists two Majorana modes in the band gap, i.e., the 30th and 31th eigenmodes. The 30th eigenmode is labeled by left mode and the 31th is labeled by right mode. (b,c) are the coefficients X30 and Y30 of the left mode, while (d,e) are the coefficients X31 and Y31 of the right mode.

Mentions: Figure 1(a) demonstrates the eigenvalues of the BdG Hamiltonian, while Fig. 1(b–e) show the distribution of the left and right Majorana zero mode, respectively. As seen in this figure, the Majorana zero mode is located near the two boundary sites of the chain. Taking a chain of length N = 30 for concreteness, we show in the following that the Majorana zero mode can be achieved by controlling the chemical potential at the two ends of the Kitaev’s chain. Consider two control Hamiltonians and , the nonzero elements of matrices Ak given by Eq. (20) corresponding to the control Hamiltonian are and .


Preparation of topological modes by Lyapunov control.

Shi ZC, Zhao XL, Yi XX - Sci Rep (2015)

The energy spectrum and spatial distributions of the BdG Hamiltonian  describing the Kitaev’s chain with total number N = 30 of sites. We have set the lattice spacing as units. There exists two Majorana modes in the band gap, i.e., the 30th and 31th eigenmodes. The 30th eigenmode is labeled by left mode and the 31th is labeled by right mode. (b,c) are the coefficients X30 and Y30 of the left mode, while (d,e) are the coefficients X31 and Y31 of the right mode.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4561913&req=5

f1: The energy spectrum and spatial distributions of the BdG Hamiltonian describing the Kitaev’s chain with total number N = 30 of sites. We have set the lattice spacing as units. There exists two Majorana modes in the band gap, i.e., the 30th and 31th eigenmodes. The 30th eigenmode is labeled by left mode and the 31th is labeled by right mode. (b,c) are the coefficients X30 and Y30 of the left mode, while (d,e) are the coefficients X31 and Y31 of the right mode.
Mentions: Figure 1(a) demonstrates the eigenvalues of the BdG Hamiltonian, while Fig. 1(b–e) show the distribution of the left and right Majorana zero mode, respectively. As seen in this figure, the Majorana zero mode is located near the two boundary sites of the chain. Taking a chain of length N = 30 for concreteness, we show in the following that the Majorana zero mode can be achieved by controlling the chemical potential at the two ends of the Kitaev’s chain. Consider two control Hamiltonians and , the nonzero elements of matrices Ak given by Eq. (20) corresponding to the control Hamiltonian are and .

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China.

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.

No MeSH data available.