Abstract
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We proposed a scheme to generate new class of even(odd) compass states (specic superpositions
of Wigner cat states [A. Dehghani et al., Ann. Phys. 362, 659 (2015)]), in the presence of the parity
deformed Jaynes{Cummings Hamiltonian [A. Dehghani et al., Sci. Rep. 6, 38069 (2016)] describing a
coupled system comprising a two-level atom and a cavity eld assisted by a continuous external classical
eld. Particular attention was given to analyze their non-classical properties through of the Mandel's
parameter and quadrature squeezing. The Wigner compass states (WCSs) are compared with the ordinary
ones, when the Wigner parameter becomes zero. Meanwhile generalized photon added compass states
(PAWCSs) were introduced, by excitations of a newly introduced WCSs. Along with statistical analysis of
latter case, a new theoretical framework for preparing them is suggested.
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