Phase transitions and the internal noise structure of nonlinear Schrodinger equation solitons

We predict phase transitions in the quantum noise characteristics of systems described by the quantum nonlinear Schrodinger equation, showing them to be related to the solitonic field transition at half the fundamental soliton amplitude. These phase transitions are robust with respect to Raman noise and scattering losses. We also describe the rich internal quantum noise structure of the solitonic fields in the vicinity of the phase transition. For optical coherent quantum solitons, this leads to the prediction that eliminating the peak sideband noise due to the electronic nonlinearity of silica fiber by spectral filtering leads to the optimal photon-number noise reduction of a fundamental soliton.