TY - JOUR

T1 - Quantum theory of solitons in optical fibers. I. Time-dependent Hartree approximation

AU - Lai, Yin-Chieh

AU - Haus, H. A.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - This paper is the first part of a two-part study on the quantum nonlinear Schrödinger equation [the second paper follows: Lai and Haus, Phys. Rev. A 39, 854 (1989)]. The quantum nonlinear Schrödinger equation is solved analytically and is shown to have bound-state solutions. These bound-state solutions are closely related to the soliton phenomenon. This fact has not been pursued in the literature. In this paper we use the time-dependent Hartree approximation to construct approximate bound states and then superimpose these bound states to construct soliton states. This construction enables us to study the quantum effects of soliton propagation and soliton collisions.

AB - This paper is the first part of a two-part study on the quantum nonlinear Schrödinger equation [the second paper follows: Lai and Haus, Phys. Rev. A 39, 854 (1989)]. The quantum nonlinear Schrödinger equation is solved analytically and is shown to have bound-state solutions. These bound-state solutions are closely related to the soliton phenomenon. This fact has not been pursued in the literature. In this paper we use the time-dependent Hartree approximation to construct approximate bound states and then superimpose these bound states to construct soliton states. This construction enables us to study the quantum effects of soliton propagation and soliton collisions.

UR - http://www.scopus.com/inward/record.url?scp=0001258860&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.40.844

DO - 10.1103/PhysRevA.40.844

M3 - Article

AN - SCOPUS:0001258860

VL - 40

SP - 844

EP - 853

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 2469-9926

IS - 2

ER -