Nonlinear coherent states for the Susskind-Glogower operators

Abstract

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 eigen- function problem to an arbitrary |mi initial condition. To analyze the obtained results, we plot the Husimi 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 non- linear coherent states may be modeled by propagating light in semi-infinite arrays of optical fibers.Comment: 22 pages, 8 figures, Conference Quantum Optics V, Published as: REVISTA MEXICANA DE F\'ISICA S 57 (3) 133-14