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We develop a fully quantum theoretical approach which describes the dynamicsof Frenkel excitons and bi-excitons induced by few photon quantum light in aquantum well or wire (atomic chain) of finite size. The eigenenergies andeigenfunctions of the coupled exciton-photon states in a multiatomic system arefound and the role of spatial confinement as well as the energy quantizationeffects in 1D and 2D cases is analyzed. Due to the spatial quantization, theexcitation process is found to consist in the Rabi-like oscillations betweenthe collective symmetric states characterized by discrete energy levels andarising in the picture of the ladder bosonic operators. At the same time, theenhanced excitation of additional states with energy close to the upperpolariton branch is revealed. The found new effect is referred to as theformation of Rabi-shifted resonances and is analyzed in details. Such statesare shown to influence dramatically on the dynamics of excitation especially inthe limit of large times.

Effects of spatial quantization and Rabi-shifted resonances in single  and double excitation of quantum wells and wires induced by few-photon  optical field