Quantum transfer in high-root topological insulators

Abstract

This paper focuses on the quantum state transfer in a one-dimensional (1D) high-root topological insulator (HRTI) with an arbitrary number of domains. We present the possibility of having multiple transfer processes in the same model due to the existence of various edge states in distinct energy gaps, which may benefit recent (de)multiplexing technologies. We also derived the relations between transfer times of different root models and different gaps in the same model. We show how the exponential decay in transfer time caused by the fragmentation of a parent chain into domains can be generalized to its higher-root versions while maintaining a high transfer fidelity, and how the increasing number of domain wall states leads to a higher transfer fidelity against a general disorder regime due to the topological protection inherited from the parent model.

Figures (14)

• Figure 1: Squaring process of the SSC($2$) model into the parent SSH and residual chains with hopping parameters $\{J_1,J_2,J_3,J_4\}=\{\sin\theta_1^{(2)},\cos\theta_1^{(2)},\sin\theta_2^{(2)},\cos\theta_2^{(2)}\}$. The two different edge potentials in the residual chain result from the lower coordination number of the end sites.
• Figure 2: (a) Energy spectrum of the SSC($2$) chain with $\theta_1^{(2)}=0.286479\pi$, $\theta_2^{(2)}=0.127324\pi$ and 40 unit cells under OBC. (b) Probability amplitude at each site for the positive energy left edge state $|\mathcal{L}_+^{(2)}\rangle$ and right edge state $|\mathcal{R}_+^{(2)}\rangle$. (c) Probability amplitude at each site for the negative energy left edge state $|\mathcal{L}_-^{(2)}\rangle$ and right edge state $|\mathcal{R}_-^{(2)}\rangle$. The states in (b)-(c) and respective energies in (a) are color-matched.
• Figure 3: Squaring process of the multiple-domain SSC($2$) model into the parent SSH and residual chains. The two different edge potentials in the residual chain result from the lower coordination number of the end sites.
• Figure 4: First domain wall state of the SSC(2) model with length $L=112$, $d=2$ domains with $14$ unit cells each, $\theta_1^{(2)}=0.286479\pi$, $\theta_2^{(2)}=0.127324\pi$ and the corresponding normalized weights in the parent SSH and residual chains. The size and color of the disks are proportional to their amplitude and phase, respectively.
• Figure 5: Effective model of the SSC($2$) chain with four domains.