Inverse scattering transform for two-level systems with nonzero background

Gino Biondini, Ildar R Gabitov, Gregor Kovačič, Sitai Li

Research output: Contribution to journalArticle

Abstract

We formulate the inverse scattering transform for the scalar Maxwell-Bloch system of equations describing the resonant interaction of light and active optical media in the case when the light intensity does not vanish at infinity. We show that pure background states in general do not exist with a nonzero background field. We then use the formalism to compute explicitly the soliton solutions of this system. We discuss the initial population of atoms and show that the pure soliton solutions do not correspond to a pure state initially. We obtain a representation for the soliton solutions in determinant form and explicitly write down the one-soliton solutions. We next derive periodic solutions and rational solutions from the one-soliton solutions. We then analyze the properties of these solutions, including discussion of the sharp-line and small-Amplitude limits, and thereafter show that the two limits do not commute. Finally, we investigate the behavior of general solutions, showing that solutions are stable (i.e., the radiative parts of solutions decay) only when initially atoms in the ground state dominate, i.e., initial population inversion is negative.

Original languageEnglish (US)
Article number073510
JournalJournal of Mathematical Physics
Volume60
Issue number7
DOIs
StatePublished - Jul 1 2019

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Inverse Scattering Transform
inverse scattering
Soliton Solution
solitary waves
Decay of Solutions
Rational Solutions
Pure State
population inversion
Light Intensity
Commute
determinants
General Solution
infinity
luminous intensity
System of equations
Ground State
atoms
Vanish
Inversion
Periodic Solution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Inverse scattering transform for two-level systems with nonzero background. / Biondini, Gino; Gabitov, Ildar R; Kovačič, Gregor; Li, Sitai.

In: Journal of Mathematical Physics, Vol. 60, No. 7, 073510, 01.07.2019.

Research output: Contribution to journalArticle

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