Inverse scattering transform for two-level systems with nonzero background
AffiliationUniv Arizona, Dept Math
MetadataShow full item record
PublisherAMER INST PHYSICS
CitationJ. Math. Phys. 60, 073510 (2019); https://doi.org/10.1063/1.5084720
JournalJOURNAL OF MATHEMATICAL PHYSICS
RightsCopyright © 2019 Author(s). Published under license by AIP Publishing.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractWe 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. Published under license by AIP Publishing.
Note12 month embargo; published online: 24 July 2019
VersionFinal published version
SponsorsNational Science Foundation [DMS-1615524, DMS-1615859]