Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement

Abstract

In this parer, q-deformed oscillator for pseudo-Hermitian systems is investigated and pseudo-Hermitian appropriate coherent and squeezed states are studied. Also, some basic properties of these states is surveyed. The over-completeness property of the para-Grassmannian pseudo-Hermitian coherent states (PGPHCSs) examined, and also the stability of coherent and squeezed states discussed. The pseudo-Hermitian supercoherent states as the product of a pseudo-Hermitian bosonic coherent state and a para-Grassmannian pseudo-Hermitian coherent state introduced, and the method also developed to define pseudo-Hermitian supersqueezed states. It is also argued that, for q-oscillator algebra of $k+1$ degree of nilpotency based on the changed ladder operators, defined in here, we can obtain deformed $S{U}_{q^2}(2)$ and $S{U}_{q^{2k}}(2)$ and also $S{U}_{q^{2k}}(1,1)$. Moreover, the entanglement of multi-level para-Grassmannian pseudo-Hermitian coherent state will be considered. This is done by choosing an appropriate weight function, and integrating over tensor product of PGPHCSs.

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Cited by in corpus (5)

• Bi-squeezed states arising from pseudo-bosons
• A concise review on pseudo-bosons, pseudo-fermions and their relatives
• Topological decompositions of the Pauli group and their influence on dynamical systems
• Nonlinear n-Pseudo Fermions
• Generalized Grassmann variables for quantum kit (k-level) systems and Barut-Girardello coherent states for su(r+1) algebras