Both Λ-type system and V-type one can show lasing without inyersion and inversion without lasing due to atomic coherence. Spontaneous emission noise of Λ-type laser is reduced due to coherent substraction but that of V-type laser is reduced due to coherent addition
We show that the problem of a \ensuremath{\Lambda}-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 \ensuremath{\Lambda}-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 \ensuremath{\Lambda}-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.
We present the quantum theory of a two-mode Lambda-type three level quantum-beat laser with injected atomic coherences. The lower two levels are coupled by an external classical field. The master equation and the Fokker–Planck equation are derived. Phases of the two modes are locked to a value depending on the phase of the external field, the phase of the injected coherence and the population of the lower two levels. Lasing without inversion and without threshold is found for both modes with and without injected coherences. Applying the appropriate initial atomic coherences one can switch intensities between the two modes, as well as bifurcation and multiple branching can be found when coherences among all levels are present. It is also possible to find phase bistability at a fixed intensity for one of the two modes, when high pump is applied. Strong intensity and phase noise reduction can be found in one of the modes at the expense of increased noises in the other one. Near Poissonian noise can be achieved. This research was supported by a grant of the Office of Naval Research.
Amplitude-noise reduction and diminished losses are found in a laser system in which the lower level of the usual two-level atom is replaced by a coherently prepared doublet, i.e., a \ensuremath{\lambda} quantum-beat configuration. The role of atomic coherence between the various levels and regular pumping is investigated. When a portion of the output signal is reflected from a phase-conjugate mirror and reinjected into the laser, the locking phase can be altered and a large phase-noise reduction can be obtained.