11 - Quantum theory of the laser – density operator approach

Summary

In Chapters 5 and 7 we presented a treatment of laser physics in which the light is described as a classical Maxwell field while the lasing medium is described as a collection of atoms whose dynamic evolution is governed by the Schrödinger equation. This semi-classical theory of laser behavior is sufficient to describe a rich variety of phenomena. However, there are many questions which require a fully quantized theory of the radiation. For example, the photon statistics and linewidth of the laser can be properly understood only via the full quantum theory of a laser.

The laser linewidth is an important quantity. For example, it determines the fundamental limit of operation of an active ring laser gyroscope. The first fully quantized derivation of the laser linewidth general enough to include even the semiconductor laser linewidth problem utilized a quantum noise operator approach, and is presented in chapter 12.

The photon statistical distribution for the laser is of interest for several reasons. Historically, it was initially thought by some that the statistical photon distribution should be a Bose–Einstein distribution. A little reflection shows that this can not be, since the laser is operating far from thermodynamic equilibrium. However, a different paradigm recognizes many atoms oscillating in phase produce what is essentially a classical current, and this would generate a coherent state; the statistics of which is Possionian. But, for example, the photon statistics of a typical Helium–Neon laser is substantially different from a Possionian distribution.