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

[摘要] 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 SU q 2 (2) and SU q 2 k (2) and also SU q 2 k (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.

[关键词] para-Grassmann variables;coherent state;squeezed state;pseudo-Hermiticity;entanglement