Resonant States Reveal Strong Light-matter Coupling, Unambiguously Quantifying Interaction Dynamics in Nanophotonic Cavities

Controlling light-matter interactions represents a major challenge in modern physics, and achieving strong coupling, where light and matter fully mix, unlocks exciting new possibilities for both fundamental science and technological innovation. Jan David Fischbach, Sergei Gladyshev, and Adrià Canós Valero, alongside colleagues from Karlsruhe Institute of Technology, University of Graz, and Riga Technical University, now present a new method for unambiguously quantifying the strength of these interactions. The team demonstrates that analysing the resonant states within nanophotonic cavities provides a more accurate way to distinguish between weak and strong coupling regimes than traditional methods, which rely on studying the system’s response at real frequencies. This approach reveals that light-matter coupling not only creates connections between different states, but also alters the fundamental properties of the photonic mode itself, offering a pathway towards a unified understanding of light-matter interactions in complex environments.

Combining theoretical modelling and numerical simulations, the team explores the characteristics of these resonant states and how they depend on the cavity’s design. Specifically, they analyse the spectral properties of the system, identifying distinct resonances that arise from the coherent exchange of energy between light and matter. The results demonstrate a significant enhancement of light-matter interaction within the cavities, evidenced by large splitting of the resonant states and their strong localization within the cavity structure. This strong coupling regime enables novel functionalities and opens up possibilities for advanced photonic devices and quantum technologies. The research provides insights into the fundamental physics governing light-matter interactions at the nanoscale and establishes a pathway for tailoring cavity properties to achieve desired coupling strengths and functionalities.

Resonant States and Strong Coupling Hamiltonian Derivation

This supplementary material details the theoretical framework and computational methods used to model strong light-matter coupling in a chromophoric sponge placed within an optical cavity. The core method involves expanding the system’s response in terms of its resonant states, also known as quasinormal modes. Researchers derive an effective Hamiltonian to describe the coupling between the optical cavity mode and the material resonances, allowing for the calculation of the system’s eigenfrequencies and the degree of hybridization. The team employs a multi-scale approach to model the system, involving different levels of detail for the material, cavity, and their interaction.

An inverse eigenproblem is used to extract the coupling strengths between the optical and material resonances from the calculated resonant state frequencies, essentially solving for the parameters of the effective Hamiltonian given the eigenfrequencies. The authors provide a Python implementation of this inverse eigenproblem solver, ensuring the reproducibility of their methods. Key concepts include quasinormal modes, hybridization, and effective Hamiltonians.

Resonant States Reveal Coupling Strength and Hybridization

This work establishes a new framework for understanding the strength of light-matter interactions in resonant systems, moving beyond traditional methods that rely on analysing the optical response at real frequencies. Researchers demonstrate that examining photonic resonant states allows for a clear distinction between weak and strong coupling regimes, revealing subtle effects often obscured by conventional approaches. The team developed a method that accurately quantifies the interaction strength by tracking the trajectories of these resonant states in the complex frequency plane, allowing for direct extraction of coupling rates even with multiple interacting materials. This approach reveals that hybridization not only introduces coupling between light and matter, but also shifts the inherent frequency of the photonic mode itself, a nuance often overlooked.

By applying this framework to planar and spherical silver resonators containing molecular materials, the researchers validated their model and demonstrated its ability to capture complex interactions. The findings provide a foundation for designing and interpreting light-matter interactions in complex photonic environments, with potential applications in areas such as polariton lasing, computing, and chemistry. The availability of codes and datasets associated with this study facilitates further exploration and validation by the wider research community.