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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 the Lyapunov function. It can be found that  and  imply the other quasiparticle modes being suppressed.
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f7: The dynamical evolution of system as a function of time with the Lyapunov function. It can be found that and imply the other quasiparticle modes being suppressed.

Mentions: In this case, the Lyapunov function is chosen a bit different from before, which becomes with and . Subsequently, the control field can be straightforwardly taken as . We set , while the other coefficients vanish and F1 = 1 for numerical calculation. The occupations of the left and right mode are given in Fig. 7. As expected, the Lyapunov function reaches its minimum when the system arrives at the edge mode. The final mode could be approximately written as , showing that we have realized the edge mode. Note that the occupation difference could not guarantee that the final mode converges to the edge mode, which is distinct to the aforementioned cases . As the evolution of the coefficients of the operator is unitary (see equation (22)) when B = 0, the coefficients should satisfy , i.e., it is invariant during the evolution. From the numerical calculation, we can find that the final mode can be approximately written as , indicating that the coefficients of the other quasiparticle modes almost vanish.


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 the Lyapunov function. It can be found that  and  imply the other quasiparticle modes being suppressed.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f7: The dynamical evolution of system as a function of time with the Lyapunov function. It can be found that and imply the other quasiparticle modes being suppressed.
Mentions: In this case, the Lyapunov function is chosen a bit different from before, which becomes with and . Subsequently, the control field can be straightforwardly taken as . We set , while the other coefficients vanish and F1 = 1 for numerical calculation. The occupations of the left and right mode are given in Fig. 7. As expected, the Lyapunov function reaches its minimum when the system arrives at the edge mode. The final mode could be approximately written as , showing that we have realized the edge mode. Note that the occupation difference could not guarantee that the final mode converges to the edge mode, which is distinct to the aforementioned cases . As the evolution of the coefficients of the operator is unitary (see equation (22)) when B = 0, the coefficients should satisfy , i.e., it is invariant during the evolution. From the numerical calculation, we can find that the final mode can be approximately written as , indicating that the coefficients of the other quasiparticle modes almost vanish.

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.