Abstract
We construct a new family of deformed states. These states are normalizable on the whole complex plane and continuous in their label z. Under fixed values of parameters, they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated Stieltjes power-moment problem. In addition to the mathematical characteristics, the quantum statistical properties of these states are analytically and numerically discussed in detail in the context of conventional as well as deformed quantum optics. We find that, for non-deformed photons, the states exhibit quadrature squeezing and their photon number statistics is sub-Poissonian. On the other hand, for deformed photons, the states are super-Poissonian and no quadrature squeezing occurs.
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