Abstract
At first, we introduce α-deformed algebra as a kind of generalization of the Weyl–Heisenberg algebra so that we get the su(2)- and su(1, 1)-algebras whenever α has specific values. After that, we construct coherent states of this algebra. Third, a realization of this algebra is given in the system of a harmonic oscillator confined at the center of a potential well. Then, we introduce two-boson realization of the α-deformed Weyl–Heisenberg algebra and use this representation to write α-deformed coherent states in terms of the two modes number states. Following these points, we consider mean number of excitations (we call them in general photons) and Mandel parameter as statistical properties of the α-deformed coherent states. Finally, the Fubini–Study metric is calculated for the α-coherent states manifold.
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