Quantum-optical excitations of semiconductor nanostructures in a microcavity using a two-band model and a single-mode quantum field

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.