ua nt - p h / 99 04 10 4 v 1 2 9 A pr 1 99 9 Phase transitions and the internal noise structure of nonlinear Schrödinger equation solitons

We predict phase-transitions in the quantum noise characteristics of systems described by the quantum nonlinear Schrödinger 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 side-band noise due to the electronic nonlinearity of silica fiber by spectral filtering leads to the optimal photon-number noise reduction of a fundamental soliton. 1 An initially localized wavepacket oscillates or " breathes " as it evolves into a soliton in a system described by a nonlinear Schrödinger equation. For the special case of integral multiples of the fundamental soliton amplitude, this oscillation is periodic. Otherwise, the wavepacket asymptotically evolves into an integral order " higher-order " soliton or if the initial wavepacket energy is near that of a fundamental soliton, the oscillatory breathing motion decays. The underlying physics is that the spectrum broadens due to the self-phase modulation and the dispersion acts as a feedback mechanism to redirect energy to the pulse center. A characteristic signature of soliton formation for pulses more energetic than the fundamental soliton (that is, for N > 1) is the bifurcation and rejoining that occurs in the wavepacket spectral domain. Breathing oscillations occur for N < 1 but no distinct bi-furcation in the intensity spectrum occurs. (Note, we take N = 1 as the amplitude of a fundamental soliton.) When bright solitons do not exist (e.g., for normal dispersion), there is no feedback mechanism and the energy is transported away from the pulse center. Similarly , for N < 0.5 in the anomalous dispersion regime, no soliton emerges in the asymptotic field. An important property of the soliton system is that for N > 0.5 the asymptotic field contains one or more fundamental solitons [1]. The nonlinear Schrödinger equation therefore predicts a phase-transition in the asymptotic field at N = 0.5 from 0 → 1 solitons. The soliton physics which leads to this behavior has important consequences which have not been previously explored. For example, below the phase-transition, quantum effects are small, whereas above the transition, they play an important role in structuring the noise properties of optical pulses. Recent quantum noise experiments with optical solitons …