No abstract

We study the topological optical states in one-dimensional (1D) dimerized ultracold atomic chains, as an extension of the Su-Schrieffer-Heeger (SSH) model. By taking the fully retarded near-field and far-field dipole-dipole interactions into account, we describe the system by an effective non-Hermitian Hamiltonian, vastly different from the Hermitian Hamiltonian of the conventional SSH model. We analytically calculate the complex bandstructures for infinitely long chains, and show that the topological invariant, i.e., the complex Zak phase, is still quantized and becomes nontrivial when the dimerization parameter β > 0.5, despite the broken chiral symmetry and non-Hermiticity. We have verified the validity of the bulk-boundary correspondence for this non-Hermitian system by further analyzing the eigenstate distributions along with their inverse participation ratios (IPRs) for finite chains, where topologically protected edge states are unambiguously identified. We also reveal that such topological edge states are robust under symmetry-breaking disorders. For transverse eigenstates, we further discover the increase of localization length of topological edge states with the increase of lattice period due to the presence of strong far-field dipole-dipole interactions. Moreover, the ultra-strong scattering cross section and ultra-narrow linewidth of a single cold atom allow us to observe in more detail about topological states than in conventional systems, such as the frequency shift with respect to the single-atom resonance and the largely tunable bandgap. We envisage these topological photonic states can provide an efficient interface between light and matter.

Topological phonon polaritons (TPhPs) are highly protected and localized edge modes that are capable of achieving a strong confinement of electromagnetic waves and immune to impurities and disorder. Here we realize TPhPs by constructing one-dimensional dimerized silicon carbide nanoparticle chains, which mimic the topological property of the well-known Su-Schrieffer-Heeger (SSH) model. We analytically calculate the complex band structure of such chains by taking all nearfield and far-field dipole-dipole interactions into account. For longitudinal modes, we demonstrate that, despite the non-Hermiticity and breaking of the chiral symmetry, the band topology can be still characterized by the complex Zak phase, which is quantized and indicates a topological phase transition when the dimerization parameter β changes from less than 0.5 to larger than 0.5, like the conventional Hermitian SSH model. By calculating the eigenmodes of a finite chain, we find such a dimerized chain with β > 0.5 supports nontrivial topological eigenmodes localized over both of its edges, indicating the validity of the bulk-boundary correspondence. On the other hand, for transverse modes, we discover a topological phase transition by increasing the lattice constant, which is due to the presence of strong long-range far-field dipole-dipole interactions decaying with the distance r as 1/r for an infinitely long chain. However, we surprisingly find the emergence of non-Hermitian skin effect in a finite chain, which leads to the breakdown of the bulk-boundary correspondence. Furthermore, by incorporating the effect of localized bulk eigenmodes and proposing a modified complex Zak phase for a finite lattice, we still recover the topological behavior of the conventional SSH model. Our comprehensive study provides profound implications to the fields of non-Hermitian topological physics and quantum mechanical models with long-range interactions. In addition to the theoretical analysis, we demonstrate the excitation of the topological phonon polaritons and show their enhancement to the photonic LDOS. These TPhPs offer an efficient tool for enhancing light-matter interaction in the mid-infrared. arXiv:1807.08276v3 [cond-mat.mes-hall]