Nonclassical properties of two families of q-coherent states in the Fock representation space of q-oscillator algebra

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 1. Their positive definite q-measures are different, but in the limit q -> 1 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.