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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.
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