Quantum fluctuations in small lasers

Master equations are used to demonstrate the dominant role of quantum fluctuations in determining the steady-state and transient response of a laser when there is a small number of particles in the system. In this regime, quantum fluctuations are found to suppress the lasing threshold and create a non-Poisson probability distribution for $n$ discrete excited electronic states and $s$ discrete photons. The correlation between $n$ and $s$ damps the averaged dynamic response of laser emission. Random walk calculations verify the master equation predictions and are used to connect to systems containing larger numbers of particles.