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- Title
Arik-Coon -oscillator cat states on the noncommutative complex plane and their nonclassical properties.
- Authors
Fakhri, H.; Sayyah-Fard, M.
- Abstract
The normalized even and odd -cat states corresponding to Arik-Coon -oscillator on the noncommutative complex plane are constructed as the eigenstates of the lowering operator of a -deformed algebra with the left eigenvalues. We present the appropriate noncommutative measures in order to realize the resolution of the identity condition by the even and odd -cat states. Then, we obtain the -Bargmann-Fock realizations of the Fock representation of the -deformed algebra as well as the inner products of standard states in the -Bargmann representations of the even and odd subspaces. Also, the Euler's formula of the -factorial and the Gaussian integrals based on the noncommutative -integration are obtained. Violation of the uncertainty relation, photon antibunching effect and sub-Poissonian photon statistics by the even and odd -cat states are considered in the cases and .
- Subjects
NONLINEAR oscillators; NONCOMMUTATIVE differential geometry; EIGENVALUES; INTEGRALS; EULER equations (Rigid dynamics); MATHEMATICAL formulas; PHOTON statistics
- Publication
International Journal of Geometric Methods in Modern Physics, 2017, Vol 14, Issue 4, p-1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887817500608