DYNAMIC NOISE-REDUCTION IN MULTILEVEL LASERS - NONLINEAR-THEORY AND THE PUMP-OPERATOR APPROACH

We present a general theory that connects the pump process in multilev el lasers with the statistics of the laser field. The key ingredient i n our approach is the derivation of an effective master equation that involves only the two laser levels and that contains a non-Markovian p ump term. This pump term gives rise to a narrowing of the photon-numbe r distribution in Steady state. The qualitative features of this dynam ic noise reduction can be inferred from the eigenvalues of the pump te rm, which are known analytically. As the mechanism that is responsible for the noise reduction, we identify a correlated excitation process in which the effective excitation rate from the lower to the upper las er level depends on the photon number. This correlated excitation proc ess is very different from an excitation at equidistant times, such as in lasers with periodic external injection. We stress that our approa ch is general and the treatment nonlinear because we do not resort to approximations such as an adiabatic elimination of atomic variables or the linearization of a Fokker-Planck equation. It is therefore partic ularly relevant for the description of systems where the active medium consists of a few atoms only and where the field losses are not negli gible on the time scale of the atomic relaxations. This would be the c ase in an ion-trap laser. For such a situation our results are substan tially different from those obtained by a linearized treatment.