Statistical fractional-photon squeezed states

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Abstract
We construct a large class of squeezed states realized in terms of density matrices. The moments of the canonical variable q^ and the number operator n^ distributions are analytically evaluated. The new states can be simultaneously squeezed in q^ and n^ to any desired amount and exhibit almost Gaussian shape in the former and strongly sub-Poisson distribution in the latter. The probability distributions can be synthetically characterized in terms of the fractional-photon index introduced by Katriel, Rassetti, and Solomon [Phys. Rev. D 35, 1248 (1987)].