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Metriplectic Structure of a Radiation-Matter-Interaction Toy Model.

Massimo Materassi1,2, Giulia Marcucci3,4,5, Claudio Conti4,5

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Entropy (Basel, Switzerland)
|April 23, 2022
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Summary

This study presents a metriplectic system for two-photon absorption, detailing radiation-matter coupling and leading to atomic excitation and radiation disappearance. The research applies a novel formalism to nonlinear optics.

Keywords:
Madelung variablesasymptotically stable equilibriumdissipative systemsmetriplectic systemstwo-photon absorption

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Area of Science:

  • Nonlinear Optics
  • Quantum Optics
  • Theoretical Physics

Background:

  • Metriplectic systems model dissipative dynamics using a Leibniz bracket and free energy.
  • These systems typically involve a Poisson bracket for Hamiltonian dynamics and a metric tensor for dissipation.
  • Understanding radiation-matter interactions is crucial in nonlinear optics.

Purpose of the Study:

  • To disclose a metriplectic system for a simplified two-photon absorption process in a two-level atom.
  • To analyze the radiation-matter coupling within this framework.
  • To pave the way for applying metriplectic formalism to other irreversible processes in nonlinear optics.

Main Methods:

  • Describing the system using real-imaginary decomposition of the electromagnetic field phasor.
  • Rewriting the metriplectic system in terms of Madelung variables (phase-amplitude pair).
  • Utilizing a Hamiltonian component for free electromagnetic radiation and a metric component for dissipation.

Main Results:

  • The metriplectic system successfully models the two-photon absorption process.
  • The metric component effectively encodes radiation-matter coupling.
  • The system drives towards an asymptotically stable state with atomic excitation and vanished radiation.

Conclusions:

  • The developed metriplectic system provides a robust model for two-photon absorption.
  • This work demonstrates the utility of the metriplectic formalism in nonlinear optics.
  • The findings open avenues for studying other irreversible optical processes.