Nonclassical properties of two families of q-coherent states in the Fock representation space of q-oscillator algebra
Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, P. O. Box 51666-16471, Tabriz, Iran
Accepted: 4 February 2020
Published online: 18 February 2020
We clarify that the q-generalization of the simple harmonic oscillator to the Arik–Coon one leads us to obtain two different families of q-coherent states in a Fock representation space of the system. They are eigenstates of unbounded and bounded annihilation operators associated with the Arik–Coon q-oscillator. The first family satisfies the resolution of identity condition on all the complex plane and the second one on a disc in radius . Their positive definite q-measures are different, but in the limit both of them convert to the measure of well-known coherent states for the simple harmonic oscillator. The first and second families of the q-coherent states are also deformed eigenstates of the bounded and unbounded annihilation operators, respectively. Thus, it is possible to study the statistical properties of both q-coherent states via both bounded and unbounded operators. The nonclassical behaviours of interest in this article are signal-to-quantum noise ratio, sub-Poissonian photon statistics, photon antibunching, quadrature squeezing effect and bipartite entanglement for the two families of the q-coherent states, as well as Hillery-type higher-order squeezing for their corresponding photon-added states.
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