Quantum-trajectory description of laser noise with pump depletion

Abstract

The intensity fluctuations of a three-level laser are known to drop below shot noise in the presence of depletion of the ground state. We study the fluctuations of the laser output as a function of the parameter $\ensuremath{\varepsilon},$ defined as the fraction of atoms needed for the laser to operate. For a sufficiently small number of active atoms, the value of $\ensuremath{\varepsilon},$ and thereby the ground-state depletion, can be appreciable even for modest pumping. This suggests that the intensity fluctuations in the laser output would decrease below shot noise as the number of active atoms is reduced. A microscopic approach that uses a quantum-trajectory method and a macroscopic approach using semiclassical rate equations both show, however, that rather than decreasing, the intensity fluctuations actually increase with $\ensuremath{\varepsilon}.$ We find that the fluctuations of the output are determined by the dependence of the cycle time of the atoms on the number of photons in the laser mode.