Topology and Spectral Entanglement in Cavity-Mediated Photon Scattering Reveals Links Between Band Geometry and Light-Matter Correlations

The interplay of light and matter takes a fascinating turn in recent work exploring how topology influences photon scattering, a phenomenon with potential applications in advanced optical devices. Eric R. Bittner from the University of Houston and Andrei Piryatinski from Los Alamos National Laboratory investigate cavity-mediated interactions within a topological insulator, utilising a theoretical framework that reveals a strong connection between a material’s band structure and the resulting light-matter correlations. Their work demonstrates that fourth-order interactions govern spectral entanglement and introduce Kerr nonlinearity, ultimately leading to a novel nonlinear topological phase diagram. This achievement establishes a fundamental link between band geometry and the emergence of these crucial light-matter interactions, paving the way for new approaches to manipulating light and designing materials with tailored optical properties.

The research computes how electrons respond to exchanged photons, identifying limits on how the material’s electronic bands are altered by these interactions. These results link the arrangement of electronic bands to the emergence of strong light-matter correlations, inspiring parallel developments in photonics where topological effects can be engineered to control optical response, particularly in nonlinear or quantum regimes.

Feschbach Method Maps Cavity Photon Self-Energy

Scientists developed a sophisticated method to investigate light-matter interactions within a topological insulator, employing a theoretical framework based on simplified electron interactions and a diagrammatic approach. This method formally solves the Schrödinger equation, determining how cavity photons are altered by virtual electron-hole pair excitations, denoted as ΣR(ω). The calculation incorporates the momentum of electrons and the topological phase of the material, accounting for the influence of the material’s band structure and the strength of the light-matter coupling. Researchers used this alteration to determine how photons behave within the cavity, accounting for the renormalization of the cavity mode due to its interaction with the material. To explore nonlinear optical properties, the team solved a self-consistent equation to determine the cavity resonance frequencies as a function of photon number, accurately reproducing expected polariton dispersion relations and revealing shifts in the absorption spectrum related to the underlying geometric topology of the electronic bands.

Topological Insulator Enhances Photon-Photon Interactions

Scientists have developed a quantum electrodynamical theory to describe cavity-mediated photon-photon interactions within a one-dimensional topological insulator, utilizing a simplified model of electron interactions. This work centers on calculating the fourth-order interaction vertex, Γ(4)(ω1, ω2; ω3, ω4), which governs biphoton scattering and reveals how photons interact within the material. The team constructed this vertex diagrammatically, considering polarization effects and electron-hole interactions to account for resonant and off-resonant contributions. Measurements of the photon self-energy, ΣR(ω), show it arises from virtual electron-hole excitations, reflecting both the topological phase and the spectral structure of electronic transitions. Data shows the spectral entanglement of the resulting biphoton state is primarily governed by local band geometry and momentum-space coherence, indicating that the arrangement of energy bands within the material plays a crucial role in entanglement. Applying a mathematical approximation, scientists identified dominant contributions to the scattering vertex, analyzing how curvature and dipole structure modulate non-separability, and demonstrated that the magnitude and sign of the interband current are crucial in determining both linear optical absorption and the nonlinear photon-photon interaction vertex.

Band Structure Governs Photon Scattering and Entanglement

This work presents a diagrammatic theory describing how light interacts with electrons in a topological insulator, revealing a fourth-order interaction that governs how photons scatter. The analysis demonstrates a connection between the material’s band structure and the resulting optical nonlinearity, showing how the shape and curvature of the electronic bands influence the behaviour of light. The findings indicate that local features of the band structure, such as curvature, play a dominant role in photon scattering and spectral entanglement. While the study focused on bulk material properties, future research will investigate the interplay between bulk and edge effects, particularly in nanostructured systems, to contribute to a deeper understanding of light-matter interactions and provide a foundation for designing novel optical devices.