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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 initial mode .
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f3: The dynamical evolution of system as a function of time with initial mode .

Mentions: For a finite length N of the Kitaev’s chain, there exists a weak interaction between the left and right mode with the interaction strength λ ∝ e−N/ξ29, where ξ is the coherence length. Obviously, the left and right modes are degenerate when N/ξ    1. Therefore, it is impossible to drive an initial mode into one of the Majorana zero mode individually, if the initial mode includes both the creation and annihilation operators at the same site. However, when the initial mode can be represented by with constraint that Dj(0) = 0 if Cj(0) ≠ 0 or Cj(0) = 0 if Dj(0) ≠ 0, it might be possible to drive the initial mode into one of the Majorana zero mode. Figure 3 shows this possibility for driving the system into the right mode while the initial mode is with . As expected, it converges to the right mode asymptotically.


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 initial mode .
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: The dynamical evolution of system as a function of time with initial mode .
Mentions: For a finite length N of the Kitaev’s chain, there exists a weak interaction between the left and right mode with the interaction strength λ ∝ e−N/ξ29, where ξ is the coherence length. Obviously, the left and right modes are degenerate when N/ξ    1. Therefore, it is impossible to drive an initial mode into one of the Majorana zero mode individually, if the initial mode includes both the creation and annihilation operators at the same site. However, when the initial mode can be represented by with constraint that Dj(0) = 0 if Cj(0) ≠ 0 or Cj(0) = 0 if Dj(0) ≠ 0, it might be possible to drive the initial mode into one of the Majorana zero mode. Figure 3 shows this possibility for driving the system into the right mode while the initial mode is with . As expected, it converges to the right mode asymptotically.

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.