Annual Meeting Optical Society of America

Quantum mechanical stability of solitons

Franz X. Kärtner, H. A. Haus

Published Jan 1, 1992• 0 citations

Abstract

Solitons of the classical nonlinear Schrödinger equation are stable to noise perturbations. One may ask whether the uncertainties associated with the quantum description of a soliton could cause the soliton to become unstable and to break up. It is not difficult to derive the fact that the first order soliton disperses, so that the probability of detecting the soliton at a specified position approaches zero as the time of propagation approaches infinity. This fact does not prove or disprove breakup. It can be shown by using the formalism of Ref. 1 that the intensity correlation function of a quantum soliton is time independent.2 In this paper we describe a form of a Hanbury, Brown, and Twiss experiment that could demonstrate the stability of the fundamental soliton (in principle), and we develop expressions for the hierarchy of correlation functions measured by such an experimental setup. If the soliton breaks up, the correlation functions should show a strong dependence on the propagation time of the soliton. The calculations demonstrate that all the measurable correlation functions do not depend on the propagation time; therefore the quantum soliton is stable.

DOI: 10.1364/oam.1992.fi3

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