Abstract
We develop a general approach to building photon-added generalized Peremolov coherent states (PAGPCSs) and photon-added generalized Barut-Girardello coherent states (PA-GBGCSs) associated to generalized su(1, 1) algebra. We study the problem of completeness of these coherent states for some particular cases and investigate the physical properties of these states through the evaluation of the Mandel parameter using an alteration of the Holstein-Primakoff realization of the su(1, 1) algebra. We show that these states exhibit sub-Poissonian, Poissonian, or super-Poissonian statistics. These features make the photon-added approach a good candidate for implementation of quantum optics schemes and coherent information processing.