We consider cavity-enhanced single-photon generation from stimulatedtwo-photon Raman processes in three-level systems. We compare four fundamentalsystem geometries in photon-emission configuration, one $\Lambda$-shaped, oneV-shaped and two ladder- ($\Xi$-) shaped arrangements. These can be realized assubsystems of a single quantum dot or of quantum-dot molecules. For a newmicroscopic understanding of the Raman process, we analyze the Heisenbergequation of motion applying the cluster-expansion scheme. Within this formalisman exact and rigorous definition of a cavity-enhanced Raman photon via itscorresponding Raman correlation is possible. This definition for exampleenables us to systematically investigate the on-demand potential ofRaman-transition-based single-photon sources. The four system arrangements canbe divided into two subclasses, $\Lambda$-type and V-type, which exhibitstrongly different Raman-emission characteristics and Raman-emissionprobabilities. Moreover, our approach reveals whether the Raman path generatesa single photon or just induces destructive quantum interference with otherexcitation paths. Based on our findings and as a first application of ourframework, we gain a more detailed understanding of experimental data from theliterature. Our analysis and results are also transferable to the case ofatomic three-level-resonator systems, and can be extended to more complicatedmulti-level schemes.
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