# Q-Representation of Number States

Q-Representation of Number States

Quasi-probability densities represent the density operator of optical fields. Here the special quasi-probability densities are plotted as functions of and for the first eleven photon numbers . The complex variable is an eigenvalue of the non-Hermitian annihilation operator . The number state 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 photons.

ρ

Q(α,α,n)=exp-|α||α|/(πn !)

*

2

2n

Reα

Imα

n=0,1,…,10

α

a

|n>

n