Non-hermitian Bethe-Salpeter Equation Reveals Exceptional Points in Excitonic Spectra of Open Systems

Excitons, quasiparticles formed when electrons bind to holes in materials, experience significant alterations in open systems where energy dissipates into the environment, fundamentally changing their behaviour and properties. Zhenlin Zhang, Wei Hu, and Enrico Perfetto, alongside colleagues, from the University of Science and Technology of China and the Università di Roma Tor Vergata, now present a new theoretical framework based on a generalized Bethe-Salpeter equation that accurately models these ‘non-Hermitian’ excitons from first principles. This method incorporates energy dissipation while maintaining the correct cause-and-effect relationships, allowing the team to predict the emergence of exceptional points, singularities in the excitonic spectrum, in materials like transition metal dichalcogenides interacting with light. The research reveals that these exceptional points dramatically influence valley polarization and photoluminescence, potentially enabling the design of materials with tailored optical and topological properties and establishing a powerful new approach to controlling excitonic behaviour in engineered environments.

TMDs, Valleytronics and Light-Matter Interactions

This research investigates two-dimensional materials, particularly transition metal dichalcogenides, and their interactions with light and energy. Scientists are harnessing unique properties, such as valley polarization, for advanced technologies, focusing on the creation and study of exciton-polaritons, hybrid particles formed from the strong coupling of excitons and light, which hold promise for novel optical devices and Bose-Einstein condensation in solid-state systems. Researchers are also exploring non-Hermitian physics, where energy loss or gain leads to unusual phenomena like exceptional points and altered topological properties. The work centers on understanding how light interacts with these materials, especially when placed within optical cavities to enhance these interactions.

Scientists utilize structured light, including light with orbital angular momentum, to control material properties and resulting exciton-polaritons. Key concepts under investigation include valley polarization, enabling valley-based devices, and circular dichroism, a technique used to probe this polarization. Researchers meticulously study exciton relaxation, the process by which excited excitons lose energy, as it directly impacts device efficiency. This research suggests several promising avenues for future development, including valleytronic devices, transistors, logic gates, and sensors, based on valley polarization.

Scientists are also working on polariton lasers and amplifiers with lower operating thresholds and exploring exciton-polaritons as qubits for quantum information processing. Furthermore, researchers are investigating non-Hermitian photonics for novel optical devices and topological photonics for robust light manipulation, combining TMDs with other quantum systems to create hybrid quantum devices and developing new materials with enhanced light-matter coupling. In summary, this body of research represents a vibrant and interdisciplinary field at the intersection of materials science, quantum optics, and non-Hermitian physics. It offers opportunities for developing new materials, devices, and a deeper understanding of how light and matter interact, with a strong focus on both fundamental research and potential applications.

Non-Hermitian Exciton Dynamics via Keldysh Formalism

Scientists have developed a theoretical framework to investigate excitons, bound electron-hole pairs, within open systems where energy can dissipate. This work extends traditional models of isolated systems by adapting the Bethe-Salpeter equation to account for non-Hermitian dynamics arising from interactions with the surrounding environment. The team built upon a framework for describing open quantum systems, deriving this non-Hermitian equation using diagrammatic perturbation theory on a Keldysh contour, a tool for handling time-dependent, non-equilibrium situations. This approach yields a microscopic excitonic Hamiltonian that incorporates dissipation while maintaining causality, ensuring the physical validity of the calculations.

Researchers focused on valley excitons in transition metal dichalcogenides, materials with unique electronic properties, coupled to structured photon baths, representing the electromagnetic environment surrounding the excitons. They meticulously calculated the one-particle Hamiltonian, incorporating physical potentials, dissipative effects, and decay rates to accurately model the system’s behavior. The team derived a conserving approximation by examining the conservation properties of the system, ensuring the total number of particles remains consistent with physical laws. This framework allows for the prediction and control of excitonic behavior in open systems, demonstrating how engineered environments can be used to induce and manipulate non-Hermitian and topological properties. The calculations revealed a rich landscape of exceptional points in momentum space, forming either discrete sets or continuous manifolds depending on the photon bath structure, leading to unusual polarization patterns in photoluminescence and nontrivial topological signatures.

Excitons in Open Quantum Systems Revealed

Scientists have developed a first-principles framework for understanding excitons, bound states of electrons and holes, in open quantum systems where energy loss and environmental coupling are significant. This work extends the capabilities of the Bethe-Salpeter equation to describe excitons interacting with dissipative environments while preserving causality. The team derived a microscopic excitonic Hamiltonian that accurately incorporates dissipation, enabling quantitative predictions of excitonic behavior beyond traditional closed-system treatments. Applying this formalism to valley excitons in transition metal dichalcogenides coupled to structured photon baths, researchers uncovered a rich landscape of exceptional points in momentum space.

Depending on the bath structure, these points manifest either as discrete sets or continuous manifolds. Experiments reveal that these exceptional points induce non-analytic valley-polarization, leading to unusual polarization patterns in photoluminescence and nontrivial topological signatures. The team investigated baths of both linearly and circularly polarized photons carrying orbital angular momentum, observing distinct arrangements of exceptional points depending on the bath characteristics. Measurements confirm the emergence of these unique phenomena even with weak exciton-photon coupling, demonstrating that bath engineering can effectively control and tailor excitonic behavior. The results demonstrate that the developed framework accurately predicts excitonic phenomena in open quantum materials, offering a powerful tool for designing and manipulating excitons in engineered environments.

Exciton Dissipation and Exceptional Points Revealed

Scientists have established a first-principles framework for understanding excitons, bound electron-hole pairs, in open systems where energy and particles can flow in and out. Researchers extended the Bethe-Salpeter equation to account for dissipation, representing energy loss from the system. This advancement allows for a microscopic understanding of how excitons behave in non-Hermitian environments, where traditional quantum mechanical descriptions break down. The team applied this new formalism to valley excitons in two-dimensional materials, revealing a rich landscape of exceptional points in momentum space.

These points represent singularities in the system’s behavior and give rise to unusual optical properties, including non-analytic polarization and unique photoluminescence patterns. Importantly, the presence of these exceptional points also indicates nontrivial topological characteristics, suggesting potential for controlling excitonic behavior through engineered environments. The researchers demonstrated that the key to describing dissipation lies in modifying only the non-interacting components of the system while preserving the rules governing diagrammatic expansions. They acknowledge that their current framework relies on certain approximations and that the complexity of real materials may require further refinements. Future work could focus on extending this approach to more complex systems and exploring the potential for manipulating excitonic properties for technological applications. The developed two-time Green’s function and screened interaction provide a means to compute absorption and emission energies, as well as dissipation-induced lifetimes, offering a comprehensive approach to understanding exciton dynamics in open systems.