WOLFRAM|DEMONSTRATIONS PROJECT

P-Representation of Laser Light

​
loss constant c
0.661
gain coefficient g
0.1
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
P(α,
*
α
)=exp(1-c)α
2
|
-gα
4
|

is plotted as a function of
Re(α)
and
Im(α)
. The complex variable
α
is an eigenvalue of the non-Hermitian annihilation operator
a
. The constants
c
and
g
represent optical damping and amplification (gain), respectively. The expression for the function
P(α,
*
α
)
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
c
and
g
on the shape of the real-valued function
P(α,
*
α
)
. The threshold condition of the laser is
c=1
.