Cat-states in the framework of Wigner–Heisenberg algebra

A one-parameter generalized Wigner–Heisenberg algebra (WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule [xˆ,pˆλ]=i(1+2λRˆ) and also highlights the dynamical symmetries of the pseudo-harmonic oscillator (PHO). The present article is devoted to the study of new cat-states built from λλ-deformed Schrödinger coherent states, which according to the Barut–Girardello scheme are defined as the eigenstates of the generalized annihilation operator. Particular attention is devoted to the limiting case where the Schrödinger cat states are obtained. Nonclassical features and quantum statistical properties of these states are studied by evaluation of Mandel’s parameter and quadrature squeezing with respect to the λλ-deformed canonical pairs (xˆ,pˆλ). It is shown that these states minimize the uncertainty relations of each pair of the su(1,1)su(1,1) components.