Selective high-order topological states and tunable chiral emission in atomic metasurfaces

Abstract

Atomic metasurfaces (AMs) provide a powerful nanophotonic platform for integrating topological effects into quantum many-body systems. In this Letter, we investigate the quantum optical and topological properties of a two-dimensional Kagome AM, going beyond the tight-binding approximation and incorporating all-to-all interactions. We reveal selective higher-order topological states with a unique dynamical ``chasing" behavior, protected by a generalized chiral symmetry and enabling efficient topological directional transfer. By introducing an impurity atom -- a giant atom -- coupled to all array atoms, we observe chiral emission patterns strongly dependent on the atomic polarization. This nonlocal coupling structure allows exploration of self-interference effects at subwavelength scales. Our findings establish AMs as a versatile platform for engineering tunable topological states and chiral quantum optical phenomena, with potential applications in customized light sources and photonic devices.

Figures (5)

• Figure 1: (a) Schematic of an AM, where a unit cell consists of sites $A$, $B$, and $C$ Red (blue) dashed lines mark the central hexagon plaquette (adjacent cell). (b)Two cases of the positions of the impurity atom above the AM. (c) Energy band structure for the array. (d) Band structure near the light cone; the insert magnifies the region around the crossing. Black dashed lines represent the light cone,i.e., the Bloch wave vector $|\boldsymbol{k }|=\sqrt{k_x^2+k_y^2}=2\pi/\lambda_0$ with the $x$-axis and $y$-axis components $k_{x,y}$. Here $\hat{\boldsymbol{\wp}}_0=\hat{\mathbf{e}}_z$, $\lambda_0=790\,$nm, $\Gamma_0=2\pi\times6\,$MHz, $d=0.1\lambda_0$, $z=0.4d$, $\Gamma_A=0.002\Gamma_0$ and $\delta=0$.
• Figure 2: Spectra of the AM versus state index with angles (a) $\theta=4\pi/9$ and (b) $\theta=\pi/2$, color-coded by the inverse participation ratio (IPR) $\sum_{j=1}^{N}|p_j|^4/(\sum_{j=1}^{N}|p_j|^2)^2$. Inserts magnify corner modes. (c) and (d) Population distributions $|p_j|^2$ correspond to (a) and (b), respectively. (e) Eigenfrequencies of the corner modes $\mathbf{S}_{A}$ (red solid), $\mathbf{S}_{B}$ (blue dashed), and $\mathbf{S}_{C}$ (magenta dotted) versus $\theta$, with shaded regions indicating the bulk. (f) Energy diagram of the three corner modes as a function of $\theta$, where the sectors $P_{abc}$ ($a,b,c=A, B, C$) indicate the ordering $\omega_{\mathbf{S}_a}>\omega_{\mathbf{S}_b}>\omega_{\mathbf{S}_c}$. Solid (dashed) boundaries correspond to directions $M_i$ ($a_i$) ($i=1,2,3$), where $a_{1,2,3}$ denote the directions of three edges of the triangular array ($\theta=m\pi+0, \pi/3, 2\pi/3$). The polarization $\hat{\boldsymbol{\wp}}_0$ is in-plane. Here $\delta=0.3$, and other parameters are the same as those in Fig. \ref{['Fig.1']}.
• Figure 3: Spectra of the AM versus spacing imbalance $\delta$ for (a) out-of-plane polarization $\hat{\boldsymbol{\wp}}_0=\hat{\mathbf{e}}_z$, (b) in-plane polarization $\theta=\pi/6$, and (c) in-plane polarization $\theta=\pi/4$. Corner modes (blue) remain separated from the bulk band (gray). Full-edge $\mathbf{F}$ (black), double-edge $\mathbf{T}_{12}$ (cyan), and single-edge modes $\mathbf{E}_{1}$ (green), $\mathbf{E}_{2}$ (magenta), and $\mathbf{E}_{3}$ (red) are shown. Population distributions of edge states $\mathbf{F}$, $\mathbf{T}_{12}$, and $\mathbf{E}_{3}$ are displayed in (d-f), respectively. Snapshots of the time evolution of the edge states with $\omega_A-\omega_0=64.3\Gamma_0$, (g) at $t\Gamma_0=2$ for $\hat{\boldsymbol{\wp}}_A=\hat{\mathbf{e}}_z$, (h) at $t\Gamma_0=3.3$ for $\hat{\boldsymbol{\wp}}_A=-\hat{\mathbf{e}}_x-i\hat{\mathbf{e}}_y$, and (i) at $t\Gamma_0=3.3$ for $\hat{\boldsymbol{\wp}}_A=\hat{\mathbf{e}}_x-i\hat{\mathbf{e}}_y$. Here $\delta=0.6$, and other parameters are the same as those in Fig. \ref{['Fig.1']}.
• Figure 4: Spectra of the AM with increasing positional disorder $\kappa$ for (a) out-of-plane polarization $\hat{\boldsymbol{\wp}}_0=\hat{\mathbf{e}}_z$, (b) in-plane polarization $\theta=\pi/6$, and (c) in-plane polarization $\theta=\pi/4$. Colors follow those in Fig. \ref{['Fig.2']}. Here $\delta=0.6$, and other parameters are the same as those in Fig. \ref{['Fig.1']}.
• Figure 5: Population distributions of the AM. (a) and (b) Distributions at $t\Gamma_0=0.3$, for a two-level impurity atom of $\omega_A-\omega_0=-3.06\Gamma_0$, with (a) $\hat{\boldsymbol{\wp}}_A=\hat{\mathbf{e}}_x$ and (b) $\hat{\boldsymbol{\wp}}_A=\hat{\mathbf{e}}_y$. (c) and (d) Distributions at $t\Gamma_0=0.45$, for a two-level impurity atom of $\omega_A-\omega_0=-3.06\Gamma_0$, with (c) $\hat{\boldsymbol{\wp}}_A=-\hat{\mathbf{e}}_x-i\hat{\mathbf{e}}_y$ and (d) $\hat{\boldsymbol{\wp}}_A=\hat{\mathbf{e}}_x-i\hat{\mathbf{e}}_y$. Distributions at $t\Gamma_0=0.17$, for a three-level impurity atom of $\omega_A-\omega_0=48.26\Gamma_0$, with (e) $B=0$ and (f) $B=20\Gamma_0$. In (a), (b), (e), and (f) [(c) and (d)], the position of the impurity atom corresponds to the upper (lower) panel in Fig. \ref{['Fig.1']}. Other parameters are the same as those in Fig. \ref{['Fig.1']}.