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

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 simplified yet exact approach, we study a one-dimensional two-band system interacting with a single-mode, two-photon quantum state within a Tavis$\unicode{x2013}$Cummings framework. By employing an exact coherent factorization scheme, the computational complexity is reduced significantly enabling numerical simulations. We also derive a simplified model which 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 which 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.