Inverse determination of light-matter coupling in disordered systems from transmittance spectra

We investigate quantum inverse problems in one-dimensional (1D) electronic disordered systems strongly coupled to optical cavities. More specifically, we consider the Anderson and the Aubry-Andre-Harper models connected to electronic reservoirs and embedded in a single-mode optical cavity. The light-matter interaction enables photon-assisted hopping processes that significantly modify the transmittance spectrum. Within the nonequilibrium Green’s function formalism, we implement an inversion-based approach capable of accurately extracting the electron-photon coupling strength directly from transmittance spectra. While cavity coupling acts as a minor perturbation within the Anderson model, yielding broad yet precise parameter estimates, its influence is markedly different in the Aubry-André-Harper model. The latter exhibits a sharp metal-insulator transition in 1D, thus resulting in more pronounced cavity-induced spectral changes. This renders even more accurate inverse solutions, offering unparalleled precision in the characterization of low-dimensional disordered systems. Altogether, our results demonstrate that the quantum inverse problem provides a robust diagnostic tool for quantum materials, particularly effective for systems exhibiting metal-insulator transitions.

💡 Research Summary

This paper addresses the quantum inverse problem of extracting the electron‑photon coupling strength in one‑dimensional disordered electronic systems that are strongly coupled to a single‑mode optical cavity. The authors focus on two paradigmatic models: the Anderson model, characterized by random on‑site potentials with disorder strength W, and the Aubry‑Andre‑Harper (AAH) model, which features a quasiperiodic on‑site potential of amplitude V and exhibits a self‑dual metal‑insulator transition at V = 2t. Both models are coupled to a cavity mode of frequency ω₀ via a Peierls substitution that modifies the nearest‑neighbor hopping term by a factor exp