Photon-added one-photon and two-photon nonlinear coherent states

From the photon-added one-photon nonlinear coherent states a†m|a, ƒ8, we introduce a new type of nonlinear coherent states with negative values of m. The nonlinear coherent states corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states |m8 and |08, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of m in detail. Finally, we investigate the photonadded two-photon nonlinear coherent states and find that they are still the two-photon nonlinear coherent states with certain nonlinear functions.