Nonlinear coherent states for the Susskind-Glogower operators

TL;DR

This paper introduces nonlinear coherent states based on Susskind-Glogower operators, revealing their nonclassical properties and potential applications in optical fiber systems.

Contribution

It constructs new nonlinear coherent states using Susskind-Glogower operators and explores their properties and physical realizations.

Findings

States exhibit amplitude squeezing and quantum interference.

States can be modeled by light propagation in optical fiber arrays.

Generalized eigenfunction solutions for arbitrary initial conditions.

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.