Photon-added nonlinear coherent states

The photon-added nonlinear coherent states, defined as a†m|α, f〉 up to a normalization constant, are still nonlinear coherent states with the nonlinear function f(N−m)[1−m/(N +1)]. Here |α, f〉 is the nonlinear coherent state with the nonlinear function f(N), N is the number operator, a is the boson creation operator and m is a non-negative integer. We introduce a new type of nonlinear coherent states with the nonlinear function f(N+m)[1+m/(N+ 1)] obtained from the photon-added 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 |m〉 and |0〉, 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. PACS: 42.50.Dv, 03.65.Fd Typeset using REVTEX email:[email protected] 1