Λ-type lasers and masers: Lasing without inversion and a vector model

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Abstract
We show that the problem of a Λ-type (and also a V-type) three-level single-mode laser (maser) is isomorphic to that of a two-level single-mode laser (maser) under the conditions of energy-level degeneracy and equal decay rates. This correspondence reveals that lasing without population inversion can occur in the Λ-type system with or without an initial atomic coherence, and also gives immediately the master equation of the laser (maser) field. We analyze in detail the operational and noise properties of a Λ-type laser using a Fokker-Planck approach. We also present a vector model to visualize the population trapping and the absorption and emission processes in such a laser (maser) system.