Abstract: The theory of the optical Stark effect is developed for quantum-size structures. The effect is due to the interaction of the electron system with intense light, whose frequency, approximately ega@, is in resonance between two subbands in the conduction band. The probe light of the frequency approximately ega falls in resonance with the adjacent transition between the ground state and the state with an electron-hole pair. In the quasi-steady-state mode, the singularities in the interband approximately ega@-light absorption spectra are related to the critical points of the bands, rearranged by the approximately ega@- light. The shape of the higher conduction band can be evaluated from the spectral positions of the singularities. In the case of two-photon interband transitions, a sharp dependence of the absorption on the light intensity is predicted. In the non-steady-state mode, the probe beam consists of two femtosecond approximately ega@-light pulses following each other with the delay time, $tau$-d$/. The dependence of energy, absorbed from the second pulse, on the $tau$-d$/ value is calculated. Under the approximately ega@-pumping, one of the two phenomena should be observed, depending on the type of band structure, namely, the decay of the induced polarization with the characteristic time approximately 1/ approximately ega$-R$/ or oscillations with the frequency approximately approximately ega$-R$/, where approximately ega$-R$/ is the Rabi frequency. The principal effect, controlling the decay of the Rabi oscillations, is the spreading of the packet of states generated by the approximately ega@-light pulse.!17
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