中国物理B ›› 2000, Vol. 9 ›› Issue (2): 131-137.doi: 10.1088/1009-1963/9/2/010

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QUANTUM GAP SOLITON IN PARAMETRIC PROCESS

李翔, 郭光灿   

  1. Center of Nonlinear Science, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:1999-07-22 出版日期:2000-02-15 发布日期:2005-06-10

QUANTUM GAP SOLITON IN PARAMETRIC PROCESS

Li Xiang (李翔), Guo Guang-can (郭光灿)   

  1. Center of Nonlinear Science, University of Science and Technology of China, Hefei 230026, China
  • Received:1999-07-22 Online:2000-02-15 Published:2005-06-10

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摘要： The Hamiltonian of the process of cascaded second harmonic generation is found from Maxwell equations. In the double-gap model and under rotating-wave and effective-mass approximations, it is quantized and the generalized quantum nonlinear Shr?dinger equation (GQNSE) is obtained. Tri-photon and quadri-photon bound states are found based on general solutions of GQNSE solved via Bethe's Ansatz method. Quantum parametric gap soliton (QPGS) solution is constructed consequently, and the existence of the double-gap QPGS is predicted for the first time.

Abstract: The Hamiltonian of the process of cascaded second harmonic generation is found from Maxwell equations. In the double-gap model and under rotating-wave and effective-mass approximations, it is quantized and the generalized quantum nonlinear Shr$\ddot{\rm o}$dinger equation (GQNSE) is obtained. Tri-photon and quadri-photon bound states are found based on general solutions of GQNSE solved via Bethe's Ansatz method. Quantum parametric gap soliton (QPGS) solution is constructed consequently, and the existence of the double-gap QPGS is predicted for the first time.

中图分类号:  (Solutions of wave equations: bound states)

  • 03.65.Ge
42.65.Hw (Phase conjugation; photorefractive and Kerr effects) 42.65.Ky (Frequency conversion; harmonic generation, including higher-order harmonic generation) 42.65.Tg (Optical solitons; nonlinear guided waves)