Three-level atom laser model with results and applications

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Abstract
We present here a fully quantum-mechanical treatment of the laser using a three-level atom model. The phase-space method employed is identical to that in a previous publication of ours [Phys. Rev. A 38, 4073 (1988)] and again results in a Fokker-Planck description of the laser without any approximations. The third level only provides extra deterministic terms and, if it is regarded as a further reservoir to the lasing levels, then the resultant stochastic equations have much improved stability. These equations are suitable for extensive theoretical analysis of both the laser and optical bistability, although in this paper we have concentrated on the adiabatically eliminated limit and calculated the leading noise terms in various regimes. However, we do use the technique of direct numerical simulation to solve exactly the full system of laser equations. The results display clearly many of the known laser characteristics.