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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 fidelity versus the chemical potential of nearest-neighbor sites of the boundaries affected by the control fields.We describe this influence by . Other parameters are the same as in Fig. 8. δ = 0.5 means that the value of control fields on the nearest-neighbor site is the half of control fields on the boundary sites.
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f9: The fidelity versus the chemical potential of nearest-neighbor sites of the boundaries affected by the control fields.We describe this influence by . Other parameters are the same as in Fig. 8. δ = 0.5 means that the value of control fields on the nearest-neighbor site is the half of control fields on the boundary sites.

Mentions: In a more realistic circumstance, individual controls on the boundary sites are difficult to implement, which means that the control on the boundary sites might affect the on-site chemical potential of their nearest neighbors. Suppose that the chemical potential of the nearest-neighbor sites, which is affected by the control fields, can be characterized by , i.e., the on-site chemical potential of 2nd and (N − 1)th site are replaced by . The results in Fig. 9 suggest that the fidelity keeps high even though the control fields have influences on the nearest-neighbor sites.


Preparation of topological modes by Lyapunov control.

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

The fidelity versus the chemical potential of nearest-neighbor sites of the boundaries affected by the control fields.We describe this influence by . Other parameters are the same as in Fig. 8. δ = 0.5 means that the value of control fields on the nearest-neighbor site is the half of control fields on the boundary sites.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f9: The fidelity versus the chemical potential of nearest-neighbor sites of the boundaries affected by the control fields.We describe this influence by . Other parameters are the same as in Fig. 8. δ = 0.5 means that the value of control fields on the nearest-neighbor site is the half of control fields on the boundary sites.
Mentions: In a more realistic circumstance, individual controls on the boundary sites are difficult to implement, which means that the control on the boundary sites might affect the on-site chemical potential of their nearest neighbors. Suppose that the chemical potential of the nearest-neighbor sites, which is affected by the control fields, can be characterized by , i.e., the on-site chemical potential of 2nd and (N − 1)th site are replaced by . The results in Fig. 9 suggest that the fidelity keeps high even though the control fields have influences on the nearest-neighbor sites.

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.