This chapter discusses the Rabi splitting and Rabi oscillation of excitons in semiconductor quantum dots and justifies their new characteristic features. Semiconductor quantum dots are considered as a promising candidate to implement the quantum state control and the quantum information processing. The discrete energy level structures owing to the three-dimensional confinement is favorable to realize an ideal two-level system, namely, the ground state and an excited state, whose superposition states can be manipulated by optical means. The exciton states have a huge transition dipole moment (~ 100 Debye) for typical size of quantum dots. The most prominent manifestation of the quantum coherence is the Rabi oscillation which represents the coherent evolution of the excitonic dipole moment. This is a key operation in the quantum state manipulation and has been achieved successfully by several groups. In this chapter, the excitonic Rabi splitting and Rabi oscillation in a single quantum dot are discussed theoretically and their new features due to the quantum interference are clarified. The mechanisms of the population relaxation and dephasing (decoherence) of excitons are discussed. A quantitative theory of the exciton dephasing due to the electronphonon interaction is developed based on the Green function formalism and is extended for application to the case of dephasing of the general nonradiative coherence.
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