Non-Hermitian Band Topology and Edge States in Atomic Lattices

We investigate the band structure and topological phases of one- and two-dimensional bipartite atomic lattices mediated by long-range dissipative radiative coupling. By deriving an effective non-Hermitian Hamiltonian for the single-excitation sector, we demonstrate that the low-energy dynamics of the system are governed by a Dirac equation with a complex Fermi velocity. We analyze the associated topological invariants for both the SSH and honeycomb models, utilizing synthetic gauge fields to break time-reversal symmetry in the latter. Finally, we explicitly verify the non-Hermitian bulk-edge correspondence by deriving analytical solutions for edge states localized at domain boundaries.

💡 Research Summary

The manuscript presents a comprehensive theoretical study of band topology and edge phenomena in atomic lattices whose inter‑site coupling is mediated by long‑range, radiative photon exchange. Starting from a microscopic model of two‑level atoms of two species (A and B) coupled to a three‑dimensional scalar photon field, the authors derive an effective non‑Hermitian Hamiltonian that acts solely on the atomic excitation subspace. The radiative nature of the interaction renders the Green’s function complex, introducing both a Lamb‑shift (real part) and a collective decay rate (imaginary part) into the on‑site terms, while the off‑diagonal terms encode long‑range hopping that decays as 1/r. By exploiting lattice translational symmetry, the atomic amplitudes are Fourier transformed, leading to a momentum‑space eigenvalue problem H(α,β)ψ=αψ where α is a dimensionless frequency and β lies in the first Brillouin zone. The Hamiltonian is expressed as H=h₀σ₀+ h·σ, with four complex coefficients h₀, h₁, h₂, h₃ that depend on the lattice sums S₀(α,β) and S±(α,β). The non‑Hermitian character is evident because all h’s are complex; h₀ contains the collective decay, while h₁–h₃ encode the effective hopping geometry.

In the weak‑coupling regime (κ_A,κ_B≪1) and for nearly degenerate atomic resonances, the nonlinear eigenvalue equation det