Nonlinear solitonic analogues of coherent and squeezed states: Graded-index fiber solitons and breathing spherically symmetric BEC clouds

Based on the symmetry reduction procedures, we introduce nonlinear solitonic analogues of coherent and squeezed states both for self-focusing and self-defocusing nonautonomous NLSE models with harmonic oscillator confining potentials. We demonstrate that chirping of the de Broglie wave is a key physical condition for the existence of squeezed states, and it is precisely this wave effect that opens the way to the fundamental extension of the squeezed state concept to different nonlinear physical systems. We show that a subtle interplay between nonlinearity and space dimensionality can result in a rich variety of nonlinear squeezed states. In one dimensional symmetry, nonlinear squeezed states are formed if and only if the nonlinear response of one-dimensional graded-index external potential (waveguide) is inversely proportional to the “hidden” squeezing parameter. And vice versa, in the case of three-dimensional symmetry, the nonlinearity is required to be proportional to the “hidden” squeezing parameter. This remarkable finding carries the germ of the idea of the 3-D soliton bullet formation and the self-focusing collapse suppression in the experimental setup arranged so that periodic variations of the nonlinearity and the maximum peaks of nonlinear squeezed states are being opposite in phases, and as the result, these two processes are alternating to each other. By means of direct computer experiments, we demonstrate the stability of soliton-like coherent and squeezed states, and reveal remarkable and complete analogies with their canonical linear progenitors.