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

Yusef Maleki

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 \(SU_{q^2}(2)\) and \(SU_{q^{2k}}(2)\) and also \(SU_{q^{2k}}(1,1)\). 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.
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)

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