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Abstract
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A one-parameter generalized Wigner–Heisenberg algebra (WHA)
is reviewed in detail. It is shown that WHA verifies the deformed
commutation rule [ˆx, ˆpλ] = i(1 + 2λˆR) 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 λ-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 λ-deformed canonical
pairs (ˆx, ˆpλ). It is shown that these states minimize the uncertainty
relations of each pair of the su(1, 1) components.
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