Adiabatic pumping of topological corner states by coherent tunneling in a 2D SSH model

TL;DR

This work addresses robust long-range transfer of topological corner states in a 2D SSH lattice by engineering a topological dark state that enables adiabatic pumping via coherent tunneling (CTAP). The authors construct a nine-state effective model within the corner/interface/center subspace and demonstrate that a pair of offset Gaussian pulses drives the system from the top-left to the bottom-right corner with high fidelity while keeping intermediate states unpopulated. Compared to a two-stage 2D Rice-Mele (Thouless) pumping, the CTAP-based scheme exhibits superior fidelity and efficiency, particularly because the dark-state evolution preserves the in-gap gap throughout the process. The approach is scalable to larger systems and adaptable to various experimental platforms, and it can be enhanced by shortcuts to adiabaticity or optimal-control methods to further reduce transfer times.

Abstract

The active manipulation of topologically protected states represents a pivotal frontier for quantum technologies, offering a unique confluence of topological robustness and precise quantum control. We propose an adiabatic pumping scheme for the long-range transfer of topological corner states in a two-dimensional Su-Schrieffer-Heeger model. The protocol utilizes a modular lattice architecture composed of four topologically distinct subblocks, enabling the modulation of a topological dark state by precise tuning of lattice couplings. This approach is based on coherent tunneling by adiabatic passage among topological corner and interface states. We establish a multi-level model for the adiabatic pumping that provides an accurate description of the underlying mechanism. In comparison with a sequential two-stage Thouless pumping, our protocol offers superior performance in both transfer fidelity and efficiency.

Figures (7)

• Figure 1: (a) Schematic illustration of the 2D tight-binding model with interfaces labeled by dashed lines. The system is constructed by connecting four 2D SSH models. The corresponding hopping rates satisfy $w_{x(y)}>v_{x(y)},v_{x(y)}'$, leading to the existence of nine topological corner states. (b) Distributions of the nine degenerate topological corner modes in the flat-band limit $v_{x(y)}=v_{x(y)}'=0$.
• Figure 2: (a) Instantaneous energy spectrum of $H(t)$ with $2L - 1 = 27$. (b) Time dependence of the hopping amplitudes. We have set $v_x=v_y$, $v_x'=v_y'$, which follow the bell-shaped function $\Omega(t) = \Omega_m \exp[-(t\pm\delta/2)^2/\lambda^2]$. The parameters are $\Omega_m = 0.9$, $\lambda = 150$, and $\delta = w/3$. Within the energy gap of the spectrum, there are nine localized states. (c) Eigenstates along the dashed line ($t = 0$) in (a). The localized states, excluding the central zero-energy (dark) state, are doubly degenerate. Probability distributions for typical states are demonstrated in (i)-(iii), which exhibit hybridization of topological corner modes and interface states.
• Figure 3: (a) Detailed behavior of the eight localized states shown in Fig. 2. Spatial probability distributions of the non-degenerate dark state are illustrated at representative times $t = -100, -25, 0, 25, 100$. The variation of the dark state clearly exhibits a smooth transition from the upper-left corner to the lower-right counterpart in the adiabatic pumping scheme. (b) Eigenstates of the effective nine-level model. The probability distributions at the same times are depicted. Here $n=3(j-1)+i$ represents the state index of the nine levels. The distribution profiles closely match those of the full model, confirming that the effective CTAP description accurately captures the topological pumping mechanism.
• Figure 4: Evolution of the occupation probabilities at the upper-left corner site $(i,j)=(1,1)$ and the lower-right corner site $(2L-1,2L-1)$. The total modulation time is $T=600$. The system is initialized with a fully localized state at $(1,1)$ and evolves according to the variation of hopping rates shown in Fig. 2.
• Figure 5: Transfer probability $P_{{2L-1},{2L-1}}(T)$ as a function of the total modulation time $T$. When $T \gtrsim 360$, the pumping achieves a transfer probability exceeding 90%. The inset depicts the behavior of the transfer probability versus system size for a fixed modulation time $T = 600$.