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arXiv:2506.22220 · Physical review. B./Physical review. B

Microscopic approach to the quantized light-matter interaction in semiconductor nanostructures: Complex coupled dynamics of excitons, biexcitons, and photons

Hendrik Rose, Stefan Schumacher, Torsten Meier

Published Dec 1, 2025• 0 citations
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Abstract

We present a microscopic and fully quantized model to investigate the interaction between semiconductor nanostructures and quantum light fields including the many-body Coloumb interaction between photoexcited electrons and holes. Our approach describes the coupled dynamics of the quantum light field and single and double electron-hole pairs, i.e., excitons and biexcitons, and exactly accounts for Coulomb many-body correlations and carrier band dispersions. Using a straightforward yet exact approach, we study a one-dimensional two-band system interacting with a single-mode, two-photon quantum state within a Tavis-Cummings framework. By employing an exact coherent factorization scheme, the computational complexity is reduced significantly enabling numerical simulations. We also derive a simplified model that includes only the bound $1s$-exciton and biexciton states for comparison. Our simulations reveal distinct single- and two-photon Rabi oscillations, corresponding to photon-exciton and exciton-biexciton transitions. We demonstrate, in particular, that biexciton continuum states significantly modify the dynamics in a way that cannot be captured by simplified models that consider only bound states. Our findings emphasize the importance of a comprehensive microscopic modeling in order to accurately describe quantum optical phenomena of interacting electronic many-body systems.

DOI
10.1103/528f-7smh

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We present a microscopic and fully quantized model to investigate the interaction between semiconductor nanostructures and quantum light fields including the many-body Coloumb interaction between photoexcited electrons and holes. Our approach describes the coupled dynamics of the quantum light field and single and double electron-hole pairs, i.e., excitons and biexcitons, and exactly accounts for Coulomb many-body correlations and carrier band dispersions. Using a straightforward yet exact approach, we study a one-dimensional two-band system interacting with a single-mode, two-photon quantum state within a Tavis-Cummings framework. By employing an exact coherent factorization scheme, the computational complexity is reduced significantly enabling numerical simulations. We also derive a simplified model that includes only the bound 1s1s1s-exciton and biexciton states for comparison. Our simulations reveal distinct single- and two-photon Rabi oscillations, corresponding to photon-exciton and exciton-biexciton transitions. We demonstrate, in particular, that biexciton continuum states significantly modify the dynamics in a way that cannot be captured by simplified models that consider only bound states. Our findings emphasize the importance of a comprehensive microscopic modeling in order to accurately describe quantum optical phenomena of interacting electronic many-body systems.
The dynamics of semiconductor quantum wires and wells that are coupled to a single-mode quantum field are analyzed. Within a two-band tight-binding model the Coulomb interaction between electrons and holes is included on a microscopic basis and the light-matter interaction is quantized. The dynamics of the system is described by equations of motion for the relevant set of expectation values of the coupled electronic-photonic system. Starting from the initial condition of a single photon occupying the field mode, we study the dynamics of the mean photon number. To analyze effects arising from the many-body Coulomb interaction, we use an exact truncation of the electronic hierarchy problem by employing the fact that N photons cannot excite more than N electron-hole pairs. We compare Rabi oscillations with and without Coulomb interaction for different excitation conditions. When the quantum field mode is initially occupied by two photons, two interacting electron-hole pairs, i.e., biexcitons, can be generated which characteristically modify the dynamics. Within a consistent and fully-quantized approach we show consequences of biexcitonic many-body correlations that are coupled to a quantum field and discuss the obtained dynamics.
Excitons are bound electron-hole pairs in semiconductors whose interactions influence optical properties and determine their collective behavior and emergent correlated phases. Despite the theoretical and experimental significance of these phenomena, a microscopic theory of exciton-exciton interactions that takes into account the full composite nature of these quasiparticles in systems with an arbitrary single-particle Hamiltonian is lacking. Here, we present a general theory of exciton-exciton interactions that builds upon our previous publication [Physical Review B 113, 155440 (2026)], which applied only to conventional semiconductors with weak band hybridization. By contrast, the theory presented here is valid in virtually any crystalline semiconducting system and can be applied to the study of biexciton formation and correlated excitonic phases in systems where band topology, quantum geometry, and moiré effects play a significant role. In addition to the analytical theory, we also present results in simple systems with flat bands with a nontrivial quantum metric and show that the biexcitonic spectrum differs strongly from that in the case without quantum geometry. Our theory paves the way for accurate quantitative calculations of biexciton spectra and excitonic many-body phases in modern condensed-matter systems.
We theoretically study quantum-optical properties of one- and two-dimensional semiconductor nanostructures, where the electronic band structure is described by a two-band tight-binding model. Since the focus of our work is on analyzing quantum-optical effects of systems with a continuous band structure, many-body processes like electron-electron and electron-phonon interactions are neglected. The quantum-optical interband excitations are fully incorporated and described by a Jaynes-Cummings-type model. The exciting quantum light can be a state with arbitrary photon statistics. For simplicity, the results discussed here are limited to single-photon and two-photon Fock states. Our analytical approach is based on the eigenvalue problem and can be utilized to obtain explicit expressions for the steady-state properties of the system. Numerical simulations are based on solutions of the equations of motion and allow for a more precise analysis of the dynamics and nonresonant excitations of the system. We demonstrate that during the interaction process, a collective excitation of the conduction band is formed. For nonresonant excitations, this collective dynamics results in interesting steady states, in which the resonantly addressed eigenstates are occupied. The presented model provides a framework for microscopic simulations of quantum-optically excited extended semiconductor nanostructures.
Ultrafast nonlinear optical spectroscopy is used to study the coherent dynamics of optically excited electron-hole pairs in semiconductors. Coulomb interaction implies that the optical inter-band transitions are dominated, at least at low temperatures, by excitonic effects. They are further enhanced in quantum confined lower-dimensional systems, where exciton and biexciton effects dominate the spectra even at room temperature. The coherent dynamics of excitons are at modest densities well described by the optical Bloch equations and a number of the dynamical effects known from atomic and molecular systems are found and studied in the exciton-biexciton system of semiconductors. At densities where strong exciton interactions, or many-body effects, become dominant, the semiconductor Bloch equations present a more rigorous treatment of the phenomena. Ultrafast degenerate four-wave mixing is used as a tool to study the coherent exciton dynamics, and the importance of performing transform limited spectroscopy is demonstrated throughout.