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

TL;DR

Addresses the quantum inverse problem of extracting the light–matter coupling strength $\gamma$ in disordered 1D systems embedded in a single-mode cavity from transmittance spectra $\mathcal{T}(E)$. Uses nonequilibrium Green's functions to compute $\mathcal{T}(E)$ for the Anderson model and the Aubry-Andre-Harper model, and then minimizes a misfit $\overline{\chi}(\boldsymbol{\Omega})$ with respect to $\boldsymbol{\Omega}=\{\gamma, W\}$. Finds that the inverse problem reliably recovers $\gamma$ and $W$ in the Anderson case, with accuracy improving for larger $L$, and reveals markedly sharper spectral changes and higher inversion precision in the AAH model due to its localization transition and multi-band structure, including photon-assisted hopping that fills spectral gaps. Concludes that transport-based quantum inverse methods provide a robust diagnostic tool for cavity quantum materials and can translate optical cavity parameters into electronic transport observables, paving the way for spectroscopy-driven material characterization.

Abstract

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.

Figures (9)

• Figure 1: (a) Schematic illustration of an 1D chain embedded in an optical cavity. Each horizontal line corresponds to a lattice site, with its vertical position indicating the photon number ($N$) subspace. Here, $\gamma$ defines the light-matter interaction. The 1D chain is terminated at both ends by semi-infinite leads coupled to thermal reservoirs in thermal equilibrium, which serve as source and drain, respectively. (b) Electron hopping processes are accompanied by photon emission or absorption, inducing transitions between photon number subspaces $\ket{N}$ and giving rise to an effective multi-chain structure in the combined electron-photon Hilbert space.
• Figure 2: Relative error for the integrated transmittance $\langle \ln[\mathcal{T}(E;\boldsymbol{\Omega})] \rangle$ as a function of the number of photons $N_{\rm ph}$ for (a) the Anderson model, and (b) the AAH model, at fixed $L=100$ sites, and $\gamma=0.20$. Here, we set $N_{\rm ph}=10$ as the reference result.
• Figure 3: Disorder-averaged logarithm of the transmittance, $\langle \ln \mathcal{T}(E)\rangle$, as function of the energy for $L=100$, disorder strength $W=0.5$, and different electron–photon couplings.
• Figure 4: Averaged misfit function $\overline{ \chi }$ (in arbitrary units) as a function of the electron-photon coupling $\gamma$ for the 1D Anderson model evaluated in a fixed disorder strength $W = 0.5$. The energy integration in the misfit function is performed over the window $0 < E < 2t$. The vertical dashed line highlights the true coupling $\gamma_{\rm true} = 0.15$, where the minimum of $\overline{ \chi }$ occurs.
• Figure 5: Averaged misfit function $\overline{ \chi }$ (in arbitrary units) as a function of disorder strength $W$, for the 1D Anderson model, computed for a fixed electron-photon coupling $\gamma = 0.15$. The energy integration in the misfit function is performed over the window $0 < E < 2t$. The vertical dashed line highlights the true $W_{\rm true} = 0.5$, where the minimum of $\overline{ \chi }$ occurs.