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Squeezed Coherent States in Non-Unitary Approach and Relation to Sub- and Super-Poissonian Statistics

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Document pages: 52 pages

Abstract: After developing the concept ofdisplaced squeezed vacuum states in the non-unitary approach andestablishing the connection to the unitary approach we calculate theirquasiprobabilities and expectation values in generalform. Then we consider the displacement of the squeezed vacuum states andcalculate their photon statistics and their quasiprobabilities. The expectationvalues of the displaced states are related to the expectation values of theundisplaced states and are calculated for some simplest cases which aresufficient to discuss their categorization as sub-Poissonian andsuper-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 illustratein examples their photon distributions. This shows that the notions of sub- andof super-Poissonian statistics and their use for the definition ofnonclassicality of states are problematic. In Appendix A we present the most important relations for SU (1,1) treatment ofsqueezing and the disentanglement of their operators. Some initial members ofsequences of expectation values for squeezed vacuum states are collected in Appendix E.

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