Quantum theory of solitons in optical fibers. II. Exact solution

Yin-Chieh Lai*, H. A. Haus

*Corresponding author for this work

Research output: Contribution to journalArticle

173 Scopus citations


In the preceding paper [paper I of a two-part study; Lai and Haus, Phys. Rev. A 40, 844 (1989)] we have used the time-dependent Hartree approximation to solve the quantum nonlinear Schrödinger equation. In the present paper, the eigenstates of the Hamiltonian are constructed exactly by Bethes ansatz method and are superimposed to construct exact soliton states. Both fundamental and higher-order soliton states are constructed and their mean fields are calculated. The quantum effects of soliton propagation and soliton collisions are studied in the framework of this construction. It is shown that a soliton experiences dispersion as well as phase spreading. The magnitude of this dispersion is estimated and is shown to be very small when the average photon number of the soliton is much larger than unity. The phase and position shifts due to a collision and the uncertainty of these shifts are also calculated.

Original languageEnglish
Pages (from-to)854-866
Number of pages13
JournalPhysical Review A
Issue number2
StatePublished - 1 Jan 1989

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