QUANTUM-THEORY OF SOLITONS IN OPTICAL FIBERS .2. EXACT SOLUTION
QUANTUM-THEORY OF SOLITONS IN OPTICAL FIBERS .2. EXACT SOLUTION
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DOI：
10.1103/physreva.40.854
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发表时间：
1989-07-15
影响因子：
2.9
通讯作者：
HAUS, HA
中科院分区：
文献类型：
--
作者：
LAI, Y;HAUS, HA
在前面的论文中[两部分研究的论文I; Lai和豪斯，物理评论A 40，844（1989）]，我们使用了含时哈特里近似来求解量子非线性薛定谔方程。本文用Bethe近似法精确构造出哈密顿量的本征态，并将其叠加，构造出精确的孤子态。构造了基本孤子态和高阶孤子态，并计算了它们的平均场。在此框架下研究了孤子传输和孤子碰撞的量子效应。结果表明，孤子经历色散以及相位扩展。这种色散的幅度估计，并示出是非常小的平均光子数的孤子是远远大于单位。还计算了由于碰撞引起的相位和位置偏移以及这些偏移的不确定性。
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 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.