P-Representation of Laser Light

As usual in quantum optics, the density operators of light fields can be represented by normalized real-valued functions. There are three types of functions: the -representation (Glauber–Sudarshan representation), ; the -representation, ; and the Wigner–Weyl distribution, . For example, the -representation is a diagonal representation of the density operator in terms of coherent states . is a real-valued function of the complex variable . The coherent states are eigenstates of the annihilation operator . Note that all the quasi-probability densities are not genuine probability densities, but are suitable to calculate expectation values (mean values) of ordered operator products. In this case, expectation values of all normal ordered operator products can be calculated with the help of the -representation.

Snapshot 1: laser operation below threshold:

Snapshot 2: laser operation at threshold:

Snapshot 3: laser operation above threshold: