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Physical Review A

Comment on ‘‘Definition and construction of the quantum soliton states in optical fibers’’

Demin Yao

Published Apr 1, 1996• 0 citations
Publisher

Abstract

It is pointed out that the claim of Duan and Guo [Phys. Rev. A 52, 874 (1995)] based on a reasonable definition of the quantum soliton states in optical fibers, that the superposition of momentum eigenstates with the Gaussian weight function makes the fluctuation of the position operator reduce to the minimum, is not correct. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.2901

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It is pointed out that the claim of Duan and Guo [Phys. Rev. A 52, 874 (1995)] based on a reasonable definition of the quantum soliton states in optical fibers, that the superposition of momentum eigenstates with the Gaussian weight function makes the fluctuation of the position operator reduce to the minimum, is not correct. \textcopyright{} 1996 The American Physical Society.
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 Schr\"odinger equation. In the present paper, the eigenstates of the Hamiltonian are constructed exactly by Bethe's 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.