dorsal/arxiv
View SchemaMatched Pulse Propagation in a Three-Level System
| Authors | Q-Han Park, H. J. Shin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9709003 |
| URL | https://arxiv.org/abs/solv-int/9709003 |
| DOI | 10.1103/PhysRevA.57.4643 |
Abstract
The B\"{a}cklund transformation for the three-level Maxwell-Bloch equation is presented in the matrix potential formalism. By applying the B\"{a}cklund transformation to a constant electric field background, we obtain a general solution for matched pulses (a pair of solitary waves) which 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. A nonlinear superposition rule is derived from the B\"{a}cklund transformation and used for the explicit construction of two solitons as well as nonabelian breathers. Various new features of these solutions are addressed. In particular, we analyze in detail the scattering of "invertons", a specific pair of different wavelength solitons one of which moving with the velocity of light. Unlike the usual case of soliton scattering, the broader inverton changes its sign through the scattering. Surprisingly, the light velocity inverton receives time advance through the scattering thereby moving faster than light, which however does not violate causality.
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"abstract": "The B\\\"{a}cklund transformation for the three-level Maxwell-Bloch equation is\npresented in the matrix potential formalism. By applying the B\\\"{a}cklund\ntransformation to a constant electric field background, we obtain a general\nsolution for matched pulses (a pair of solitary waves) which can emit or absorb\na light velocity solitary pulse but otherwise propagate with their shapes\ninvariant. In the special case, this solution describes a steady state pulse\nwithout emission or absorption, and becomes the matched pulse solution recently\nobtained by Hioe and Grobe. A nonlinear superposition rule is derived from the\nB\\\"{a}cklund transformation and used for the explicit construction of two\nsolitons as well as nonabelian breathers. Various new features of these\nsolutions are addressed. In particular, we analyze in detail the scattering of\n\"invertons\", a specific pair of different wavelength solitons one of which\nmoving with the velocity of light. Unlike the usual case of soliton scattering,\nthe broader inverton changes its sign through the scattering. Surprisingly, the\nlight velocity inverton receives time advance through the scattering thereby\nmoving faster than light, which however does not violate causality.",
"arxiv_id": "solv-int/9709003",
"authors": [
"Q-Han Park",
"H. J. Shin"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1103/PhysRevA.57.4643",
"title": "Matched Pulse Propagation in a Three-Level System",
"url": "https://arxiv.org/abs/solv-int/9709003"
},
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