We develop a fully quantum theoretical approach which describes the dynamics of Frenkel excitons and bi-excitons induced by few photon quantum light in a quantum well or wire (atomic chain) of finite lateral size. The excitation process is found to consist in the Rabi-like oscillations between the collective symmetric states characterized by discrete energy levels. At the same time, the enhanced excitation of high-lying free exciton states being in resonance with these 'dressed' polariton eigenstates is revealed. This found new effect is referred to as the formation of Rabi-shifted resonances and appears to be the most important and new feature established for the excitation of 1D and 2D nanostructures with final lateral size. The found new physics changes dramatically the conventional concepts of exciton formation and play an important role for the development of nanoelectronics and quantum information protocols involving manifold excitations in nanosystems.
Keywords: Rabi-shifted resonances; excitation dynamics; quantum light; semiconductor nanostructures; spatial quantization.
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