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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 (a) the uncertainties in the initial mode and (b) the perturbations in the control fields f1(t) and f2(t). Other parameters are the same as in Fig. 3. The control time is terminated when the fidelity reaches 99.15%. One can observe that the fidelity is still above 98% even though there are 10% perturbations in the control fields.
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f8: The fidelity versus (a) the uncertainties in the initial mode and (b) the perturbations in the control fields f1(t) and f2(t). Other parameters are the same as in Fig. 3. The control time is terminated when the fidelity reaches 99.15%. One can observe that the fidelity is still above 98% even though there are 10% perturbations in the control fields.

Mentions: We first examine the effect of uncertainties in the initial mode and perturbations in the control fields. Taking in the Fermi system as the initial mode without uncertainties, we can write the initial mode with uncertainties as with ε quantifying the uncertainties. The dependence of the fidelity on ε is plotted in Fig. 8(a). For the control field with perturbations, we write it as with fk(t) representing the perturbationless control field. The dependence of the fidelity on the perturbations is presented in Fig. 8(b). One can find from Fig. 8 that the fidelity is more sensitive to the uncertainties in the initial mode, while it is robust against the perturbations in the control fields. In fact, from the principle of the Lyapunov control, it is suggested that the fidelity of the control process is sensitive to the sign rather than the amplitude of the control fields. This observation can be used to understand the robustness against the perturbations in the control fields.


Preparation of topological modes by Lyapunov control.

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

The fidelity versus (a) the uncertainties in the initial mode and (b) the perturbations in the control fields f1(t) and f2(t). Other parameters are the same as in Fig. 3. The control time is terminated when the fidelity reaches 99.15%. One can observe that the fidelity is still above 98% even though there are 10% perturbations in the control fields.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f8: The fidelity versus (a) the uncertainties in the initial mode and (b) the perturbations in the control fields f1(t) and f2(t). Other parameters are the same as in Fig. 3. The control time is terminated when the fidelity reaches 99.15%. One can observe that the fidelity is still above 98% even though there are 10% perturbations in the control fields.
Mentions: We first examine the effect of uncertainties in the initial mode and perturbations in the control fields. Taking in the Fermi system as the initial mode without uncertainties, we can write the initial mode with uncertainties as with ε quantifying the uncertainties. The dependence of the fidelity on ε is plotted in Fig. 8(a). For the control field with perturbations, we write it as with fk(t) representing the perturbationless control field. The dependence of the fidelity on the perturbations is presented in Fig. 8(b). One can find from Fig. 8 that the fidelity is more sensitive to the uncertainties in the initial mode, while it is robust against the perturbations in the control fields. In fact, from the principle of the Lyapunov control, it is suggested that the fidelity of the control process is sensitive to the sign rather than the amplitude of the control fields. This observation can be used to understand the robustness against the perturbations in the control fields.

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.