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Abstract
4.9- Conclusion
We easily deduce that the relation between the mean occupation number of photons and the total variances is always satisfied in the pure squeezed vacuum state and mixed one as follows
where and are the variances with respect to and .
We can see from (4.21) that the squeezed vacuum mixed state is super-Poissonian statistics of the field. Thus, the photons in a squeezed vacuum mixed state are always bunched irrespective of the value of the energy parameter .
It is clear, from the expansion (4.51), that the Wigner function for the single-mode squeezed vacuum mixed state is a real function. This function is symmetric in the real and imaginary parts of the phase space variable . The plot of the Wigner function in the plane shows that this function takes non-positive values at some points in the phase space. On the other hand, the 3-dimensional plot of this function shows that it is in the shape of a spike of a finite height. The top of this spike is pointed, while its base is of elliptical contours. This spike increases in height by decreasing the value of the mean number of photons, , present in the coherent state of the mode. In fact, the Wigner function for the squeezed vacuum mixed state attains its maximum value at the origin of coordinates [37].