Q-Representation of Number States

photon number n

9

Quasi-probability densities represent the density operator

ρ

of optical fields. Here the special quasi-probability densities

Q(α,

*

α

,n)=exp-α

2

|

α

2n

|

(πn!)

are plotted as functions of

Reα

and

Imα

for the first eleven photon numbers

n=0,1,…,10

. The complex variable

α

is an eigenvalue of the non-Hermitian annihilation operator

a

. The number state

|n>

of the field is an energy eigenstate of the same field also. This means that in these plots the optical fields can be characterized by exactly

n

photons.