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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 .Ol and Or represent the occupations of the left and right mode, while Ol + Or approaching unit implies the other quasiparticle modes except the right and left modes are suppressed. (b,c) denote the dynamical evolution of the control fields f1(t) and f2(t), respectively.
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f2: The dynamical evolution of system as a function of time with initial mode .Ol and Or represent the occupations of the left and right mode, while Ol + Or approaching unit implies the other quasiparticle modes except the right and left modes are suppressed. (b,c) denote the dynamical evolution of the control fields f1(t) and f2(t), respectively.

Mentions: Here pi = 0, pT = − 1, and UT is the target eigenvector. Then the control field becomes and we choose Fk = 10 for the numerical calculations. Figure 2 shows the occupations of the left and right mode as a function of evolution time, where the occupation is defined by for the left mode, and for the right mode. We observe that the initial mode asymptotically converges to the Majorana zero mode with time, and the control fields almost vanish when the system arrives at the target mode. Further simulations show that this proposal works for almost arbitrary initial modes. For example, it can also be driven to the Majorana zero mode when the initial modes are with θ ∈ [0, 2π].


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 .Ol and Or represent the occupations of the left and right mode, while Ol + Or approaching unit implies the other quasiparticle modes except the right and left modes are suppressed. (b,c) denote the dynamical evolution of the control fields f1(t) and f2(t), respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: The dynamical evolution of system as a function of time with initial mode .Ol and Or represent the occupations of the left and right mode, while Ol + Or approaching unit implies the other quasiparticle modes except the right and left modes are suppressed. (b,c) denote the dynamical evolution of the control fields f1(t) and f2(t), respectively.
Mentions: Here pi = 0, pT = − 1, and UT is the target eigenvector. Then the control field becomes and we choose Fk = 10 for the numerical calculations. Figure 2 shows the occupations of the left and right mode as a function of evolution time, where the occupation is defined by for the left mode, and for the right mode. We observe that the initial mode asymptotically converges to the Majorana zero mode with time, and the control fields almost vanish when the system arrives at the target mode. Further simulations show that this proposal works for almost arbitrary initial modes. For example, it can also be driven to the Majorana zero mode when the initial modes are with θ ∈ [0, 2π].

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.