### 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 language | English (US) |
---|---|

Article number | 073510 |

Journal | Journal of Mathematical Physics |

Volume | 60 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2019 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*60*(7), [073510]. https://doi.org/10.1063/1.5084720

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 60, no. 7, 073510. https://doi.org/10.1063/1.5084720

}

TY - JOUR

T1 - Inverse scattering transform for two-level systems with nonzero background

AU - Biondini, Gino

AU - Gabitov, Ildar R

AU - Kovačič, Gregor

AU - Li, Sitai

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85069931266&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069931266&partnerID=8YFLogxK

U2 - 10.1063/1.5084720

DO - 10.1063/1.5084720

M3 - Article

VL - 60

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 7

M1 - 073510

ER -