New class of generalized photon-added coherent states and some of their non-classical properties

In this paper, we construct a new class of generalized photon added coherent states (GPACSs), |z,m〉_r by excitations on a newly introduced family of generalized coherent states (GCSs) |z〉_r (A Dehghani and B Mojaveri 2012 J. Phys. A: Math. Theor. 45 095304), obtained via generalized hypergeometric type displacement operators acting on the vacuum state of the simple harmonic oscillator. We show that these states realize resolution of the identity property through positive definite measures on the complex plane. Meanwhile, we demonstrate that the introduced states can also be interpreted as nonlinear coherent states (NLCSs), with a spacial nonlinearity function. Finally, some of their non-classical features as well as their quantum statistical properties are compared with Agarwal's photon-added coherent states (PACSs), |z,m〉. (paper)