Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 084, 20 pages      arXiv:1108.5005      https://doi.org/10.3842/SIGMA.2011.084

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

Yusef Maleki
Department of Physics, University of Mohaghegh Ardabili, Ardabil, 179, Iran

Received May 27, 2011, in final form August 19, 2011; Published online August 25, 2011

Abstract
In this paper, 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 SUq2(2) and SUq2k(2) and also SUq2k(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.

Key words: para-Grassmann variables; coherent state; squeezed state; pseudo-Hermiticity; entanglement.

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