Truncated para-Bose oscillator cat states

We present the truncated (or s-deformed) para-Bose oscillator algebra of order 𝒫 = 2λ + 1, with s being a half-integer, along with its (2s + 1)-dimensional Fock representation. The model reduces to the truncated simple harmonic oscillator and the conventional para-Bose oscillator algebras in the limiting cases where the parameters λ and s approach zero and infinity, respectively. A Fock-Bargmann realization is constructed in such a way that the creation operator is expressed as a function of both deformation parameters λ and s. Two-component orthogonal cat states are formulated through suitable superpositions of even and odd parity states within the Fock representation space. The corresponding positive-definite measures over the entire complex plane are derived in terms of Meijer's G-functions parameterized by λ and s. In addition, the nonclassical properties of the even and odd cat states are analyzed, including the manifestation of sub-Poissonian statistics, photon antibunching effect, and quadrature squeezing. We further investigate how the parameters λ and s individually influence the enhancement or suppression of entanglement in the associated quasi-Bell states.