Polarization-dependent topology in quantum emitter chains

Abstract

The role of polarization in the topology of quantum emitter chains is investigated theoretically, whereby "polarization" refers to the transition dipole moments of the emitters. We show that, if the chain is zigzag-shaped, different topological phases can be realized by adjusting the polarization direction. It turns out that long-range dipole-dipole couplings weaken the bulk-boundary correspondence, but on the other hand give rise to higher-order topological phases with four observable edge modes. We also demonstrate how the polarization orientation can be used to define an additional dimension and simulate a synthetic Chern insulator. Our findings open up a way to actively switch between various topological phases within a single arrangement of quantum emitters.

Figures (3)

• Figure 1: (a) A zigzag chain with lattice constant $a$ (colors indicating the two sublattices) of two-level systems coupled via dipole-dipole interactions, with ground (excited) state $\ket{\mathrm{g}}$ ($\ket{\mathrm{e}}$), transition frequency $\omega_0$, and angle $\varphi$ of the dipole moments relative to the $x$ axis. (b) Different orientations of the dipole moments enable different topological phases. (c) Spectrum of the Hamiltonian in Eq. \ref{['eq draft Hamiltonian']}. Shaded areas indicate different values of the winding number $\nu$. (d) Populations $|\braket{\psi|i}|^2$ as a function of site index $i$ and $\varphi$. Hereby, for each $\varphi$ we consider the state $\ket{\psi}$ with the highest amplitude on the edge $\ket{1}$. (e) Spectrum of the Hamiltonian when neglecting intrasublattice couplings. (f) Populations computed as in panel (d) for the same reduced Hamiltonian. All plots used $N=50$ atoms and $a=0.3\lambda_0$.
• Figure 2: (a) System with shifted sublattice (the original position indicated by the desaturated points). (b)-(d) Winding number and localization [cf. Eq. \ref{['eq draft loc']}] as functions of polarization angle $\varphi$ and the sublattice shifts. We used $a=0.35\lambda_0$ and $N=50$ in all plots.
• Figure 3: (a) Band structure $\omega=\omega_\pm(k,\varphi)$ of the Bloch Hamiltonian $\mathcal{H}_\mathrm{RM}(k,\varphi)$. (b) Berry curvature $F_{k\varphi}^-$ of the lower Bloch band. (c) Displacement after one pumping period as a function of $k$ [cf. Eq. \ref{['eq draft displacement']}]. The cyan (purple) area indicates states inside (outside) the light cone $|k|=k_0$ (gray dashed lines at $ak/\pi=\pm0.6$). (d) Collective decay rates $\Gamma_k(\varphi)$ computed from Eq. \ref{['eq draft collective decay rates']} for the lower band. All plots used $N=50$, $a=0.3\lambda_0$, and $\Delta_0=\Gamma_0$.