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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 dynamical evolution of system as a function of time with conventional Lyapunov technique and initial mode . (c) denotes the dynamical behavior of the Lyapunov function V.
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f5: The dynamical evolution of system as a function of time with conventional Lyapunov technique and initial mode . (c) denotes the dynamical behavior of the Lyapunov function V.

Mentions: Figure 5 shows the occupation of right mode as a function of evolution time t. It demonstrates that the operator does not completely converge to the right mode since the occupation of the right mode approaches 0.5814. On the other hand, when resolving the characteristic spectrum of the free and control Hamiltonian, one can find that the target mode is controllable for an arbitrary superposition of creation operators. Next, we adopt an implicit Lyapunov-based method to steer an arbitrary initial mode into the right mode23, where the Lyapunov function is redefined as


Preparation of topological modes by Lyapunov control.

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

The dynamical evolution of system as a function of time with conventional Lyapunov technique and initial mode . (c) denotes the dynamical behavior of the Lyapunov function V.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: The dynamical evolution of system as a function of time with conventional Lyapunov technique and initial mode . (c) denotes the dynamical behavior of the Lyapunov function V.
Mentions: Figure 5 shows the occupation of right mode as a function of evolution time t. It demonstrates that the operator does not completely converge to the right mode since the occupation of the right mode approaches 0.5814. On the other hand, when resolving the characteristic spectrum of the free and control Hamiltonian, one can find that the target mode is controllable for an arbitrary superposition of creation operators. Next, we adopt an implicit Lyapunov-based method to steer an arbitrary initial mode into the right mode23, where the Lyapunov function is redefined as

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.