TITLE:
Squeezed Coherent States in Non-Unitary Approach and Relation to Sub- and Super-Poissonian Statistics
AUTHORS:
Alfred Wünsche
KEYWORDS:
SU (1, 1) Group of Squeezing and Rotation, Wigner Quasiprobability, Unitary Approach to Squeezing, Nonclassical States, Uncertainty Matrix, Distance of States, Jacobi, Ultraspherical, Legendre and Hermite Polynomials, Poisson Statistics
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.12,
December
29,
2017
ABSTRACT:
After developing the concept of
displaced squeezed vacuum states in the non-unitary approach and
establishing the connection to the unitary approach we calculate their
quasiprobabilities and expectation values in general
form. Then we consider the displacement of the squeezed vacuum states and
calculate their photon statistics and their quasiprobabilities. The expectation
values of the displaced states are related to the expectation values of the
undisplaced states and are calculated for some simplest cases which are
sufficient to discuss their categorization as sub-Poissonian and
super-Poissonian statistics. A large set of these states do not belong to sub-
or to super-Poissonian states but are also not Poissonian states. We illustrate
in examples their photon distributions. This shows that the notions of sub- and
of super-Poissonian statistics and their use for the definition of
nonclassicality of states are problematic. In Appendix A we present the most important relations for SU (1,1) treatment of
squeezing and the disentanglement of their operators. Some initial members of
sequences of expectation values for squeezed vacuum states are collected in Appendix E.