Matched pulse propagation in a three-level system

Q. Han Park, H. J. Shin

Research output: Contribution to journalArticlepeer-review

58 Citations (Scopus)


The Bäcklund transformation for the three-level coupled Schrödinger-Maxwell equation is presented in the matrix potential formalism. By applying the Bäcklund transformation to a constant-electric-field background, we obtain a general solution for matched pulses (a pair of solitary waves) that can emit or absorb a light velocity solitary pulse but otherwise propagate with their shapes invariant. In the special case, this solution describes a steady-state pulse without emission or absorption, and becomes the matched pulse solution recently obtained by Hioe and Grobe [Phys. Rev. Lett. 73, 2559 (1994)]. A nonlinear superposition rule is derived from the Bäcklund transformation and used for the explicit construction of two solitons as well as non-Abelian breathers. Various features of these solutions are addressed. In particular, we analyze in detail the scattering of “binary solitons,” a specific pair of different wavelength solitons, one of which moves with the velocity of light. Unlike the usual case of soliton scattering, the broader soliton changes its sign after the scattering, thus exhibiting a binary behavior. Surprisingly, the light velocity soliton receives a time advance through the scattering, thereby moving faster than light, which, however, does not violate causality.

Original languageEnglish
Pages (from-to)4643-4653
Number of pages11
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number6
Publication statusPublished - 1998
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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