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

TL;DR

This paper explores q-deformed pseudo-Hermitian oscillators, introducing new coherent and squeezed states, analyzing their properties, superstates, and entanglement, with implications for deformed symmetry groups.

Contribution

It develops a framework for pseudo-Hermitian para-Grassmannian coherent and squeezed states, including superstates and entanglement, extending q-oscillator algebra and deformed symmetry groups.

Findings

Over-completeness of PGPHCSs established

Stability of coherent and squeezed states analyzed

Entanglement of multi-level PGPHCSs demonstrated

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 $SU_{q^2}(2)$ 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.