Quantum Theory of the Laser

abstract

The quantum theory of the laser was developed in the 1960s principally by the schools associated with H. Haken, W.E. Lamb and M. Lax, see [1, 2, 3, 4]. Haken and Lax independently developed sophisticated techniques to convert operator master equations into c-number Fokker–Planck equations or equivalent Langevin equations.

In this chapter we shall follow the approach of Scully and Lamb [3] to compute photon statistics and the linewidth of the laser. In the Scully–Lamb treatment the pumping is modelled by the injection of a sequence of inverted atoms into the laser cavity. In a usual laser, with a thermal pumping mechanism, a Poisson distributed sequence of inverted atoms is assumed. Introduction of a Bernoulli distribution enables a more general class of pumping mechanisms to be considered, including the case of the regularly pumped laser. Diode lasers with more regular pumping than usual lasers have recently been shown to give rise to sub-shot-noise photocurrent fluctuations.