# P-Representation of Laser Light

P-Representation of Laser Light

Quasi-probability densities are representations of the density operator ρ of optical fields. Here the special quasi-probability density of laser light near the laser threshold is plotted as a function of and . The complex variable is an eigenvalue of the non-Hermitian annihilation operator . The constants and represent optical damping and amplification (gain), respectively. The expression for the function can be derived from the equation of motion for the laser field density matrix. This so-called "master equation" considers both the interaction of active atoms, which are resonant with the single-mode laser field, and the decay of the atomic levels. This Demonstration shows the influence of the parameters and on the shape of the real-valued function . The threshold condition of the laser is .

P(α,α)=exp(1-c)|α|-g|α|

*

2

4

Re(α)

Im(α)

α

a

c

g

P(α,α)

*

c

g

P(α,α)

*

c=1