Quantum noise of the fundamental soliton

Abstract

We investigate the noise in a fundamental soliton state constructed from the exact energy eigenstates of the quantized nonlinear Schr\"odinger equation. It is shown that such a state has statistical properties that are substantially different from those of a coherent state with the same mean field. We can construct, for example, a fundamental soliton state that has initially minimum fluctuations for the four linearized soliton operators (particle number, phase, momentum, and position). We also show that the linearized noise analysis is not valid for nonlinear phase shifts larger than ${\mathit{n}}_{0}^{1/4}$, where ${\mathit{n}}_{0}$ is the average number of particles in the fundamental soliton. \textcopyright{} 1996 The American Physical Society.