Finite-dimensional even and odd nonlinear pair coherent states and their some nonclassical properties

In this paper a new class of finite-dimensional even and oddnonlinear pair coherent states (EONLPCSs), which can be realized viaoperating the superposed evolution operators $D_pm (tau )$ on thestate $left| {q,0} rightrangle $, is constructed, then theirorthonormalized property, completeness relations and somenonclassical properties are discussed. It is shown that thefinite-dimensional EONLPCSs possess normalization and completenessrelations. Moreover, the finite-dimensional EONLPCSs exhibitremarkably different sub-Poissonian distributions and phaseprobability distributions for different values of parameters $q$,$eta $ and $xi $.