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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 eigenvalue spectrum and spatial distributions of the Hamiltonian  in the SSH model with N = 21 sites.Two edge mode are found in the band gap, corresponding to the 11th and 32th eigenvectors. We label the 11th eigenvector as left mode while the 32th eigenvector is the right mode. (b) and (c) are the coefficients X11 and Y11 of the left mode while (d,e) are the coefficients X32 and Y32 of the right mode.
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f4: The eigenvalue spectrum and spatial distributions of the Hamiltonian in the SSH model with N = 21 sites.Two edge mode are found in the band gap, corresponding to the 11th and 32th eigenvectors. We label the 11th eigenvector as left mode while the 32th eigenvector is the right mode. (b) and (c) are the coefficients X11 and Y11 of the left mode while (d,e) are the coefficients X32 and Y32 of the right mode.

Mentions: where ε is a parameter to change the hoping amplitude J, 0 ≤ ε ≤ 1, and μ is the chemical potential. This model can be applied to describe bosons hopping in a double-well 1D optical lattice31. The edge mode in the topological band has been shown in Ref. 31, which can be witnessed by the nontrivial Zak phase32 of the bulk bands. Thereby it can be taken as the target mode in this control system, and we choose the parameters J = 1, μ = 2, N = 21, and ε = 0.3 for the following numerical calculation. Firstly, we present the results of exact diagonalization of 33 (see methods) in Fig. 4(a) and give the coefficients of the edge mode in Fig. 4(b–e). It can be found that the edge mode is located near the first site of the chain, this suggests us to regulate the on-site chemical potential (energy) of site 1 to manipulate the system. Namely, the control Hamiltonian is suggested to be As the Hamiltonian is block diagonal, we could drive the system from an arbitrary initial mode to the target mode for two special cases listed below.


Preparation of topological modes by Lyapunov control.

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

The eigenvalue spectrum and spatial distributions of the Hamiltonian  in the SSH model with N = 21 sites.Two edge mode are found in the band gap, corresponding to the 11th and 32th eigenvectors. We label the 11th eigenvector as left mode while the 32th eigenvector is the right mode. (b) and (c) are the coefficients X11 and Y11 of the left mode while (d,e) are the coefficients X32 and Y32 of the right mode.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: The eigenvalue spectrum and spatial distributions of the Hamiltonian in the SSH model with N = 21 sites.Two edge mode are found in the band gap, corresponding to the 11th and 32th eigenvectors. We label the 11th eigenvector as left mode while the 32th eigenvector is the right mode. (b) and (c) are the coefficients X11 and Y11 of the left mode while (d,e) are the coefficients X32 and Y32 of the right mode.
Mentions: where ε is a parameter to change the hoping amplitude J, 0 ≤ ε ≤ 1, and μ is the chemical potential. This model can be applied to describe bosons hopping in a double-well 1D optical lattice31. The edge mode in the topological band has been shown in Ref. 31, which can be witnessed by the nontrivial Zak phase32 of the bulk bands. Thereby it can be taken as the target mode in this control system, and we choose the parameters J = 1, μ = 2, N = 21, and ε = 0.3 for the following numerical calculation. Firstly, we present the results of exact diagonalization of 33 (see methods) in Fig. 4(a) and give the coefficients of the edge mode in Fig. 4(b–e). It can be found that the edge mode is located near the first site of the chain, this suggests us to regulate the on-site chemical potential (energy) of site 1 to manipulate the system. Namely, the control Hamiltonian is suggested to be As the Hamiltonian is block diagonal, we could drive the system from an arbitrary initial mode to the target mode for two special cases listed below.

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.