Squeezed Coherent States in Non-Unitary Approach and Relation to Sub- and Super-Poissonian Statistics
Alfred Wünsche · Advances in Pure Mathematics · 2017
After developing the concept of displaced squeezed vacuum states in the nonunitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values † k a a 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 ( ) 1,1 SU 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.