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Inverse scattering transform for two-level systems with nonzero background | | Gino Biondini
; Ildar Gabitov
; Gregor Kovacic
; Sitai Li
; | | Date: |
14 Jul 2019 | | 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 dominant, i.e., initial
population inversion is negative. | | Source: | arXiv, 1907.6231 | | Services: | Forum | Review | PDF | Favorites | |
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