Nonlinear coherent states for the Susskind-Glogower operators

We construct nonlinear coherent states for the Susskind-Glogower operators by the application of the displacement operator on the vacuum state. We also construct nonlinear coherent states as eigenfunctions of a Hamiltonian constructed with the Susskind-Glogower operators. We generalize the solution of the eigenfunction problem to an arbitrary vertical bar m > initial condition. To analyze the obtained results, we plot the Husitni Q function, the photon number probability distribution and the Mandel Q-parameter. For both cases, we find that the constructed states exhibit interesting nonclassical features, such as amplitude squeezing and quantum interferences due to a self-splitting into two coherent-like states. Additionally, we show that nonlinear coherent states may be modeled by propagating light in semi-infinite arrays of optical fibers.