A solution of density matrix equation for one mode of laser light

Boris Volodumurovich Bondarev

Gerald T. Moore

The propagation of light in a one-dimensional cavity bounded by moving mirrors is studied in the context of the theory of gas lasers. A canonical quantization of the free field is carried out by utilizing the symplectic structure of the space of solutions of the wave equation. It is shown that no Hamiltonian and no Schrodinger picture exists and that the photon number operator is in general not conserved. Changes in the number operator are, however, ordinarily too small to be observed experimentally. Automorphic coordinate transformations are used to develop adiabatic expansions for the mode functions of cavities with one fixed and one moving mirror. The coupling of the field to two-level atoms is done both quantum-mechanically and semi-classically. For the interacting quantum field an interaction Hamiltonian does exist, even though there is no total Hamiltonian. The semi-classical equations treat the atomic density matrix as a distribution in phase space. They possess traveling wave solutions which are expected to be important in understanding the behavior of mode-locked lasers. (Author)

Richard M. Sillitto

J. A. Fleck

We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with $N$ stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.

J. A. Fleck

We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with $N$ stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.

Hermann Haken