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Delocalization and quantum chaos in atom-field systems.

M A Bastarrachea-Magnani1, B López-del-Carpio2, J Chávez-Carlos1

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This study quantifies regular and chaotic behavior in the Dicke model, finding a strong link between classical Lyapunov exponents and quantum Participation Ratio. The ratio

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Area of Science:

  • Quantum optics
  • Atomic physics
  • Chaos theory

Background:

  • The Dicke model is a fundamental system for studying atom-field interactions.
  • Understanding the transition between regular and chaotic dynamics is crucial in quantum systems.

Purpose of the Study:

  • To quantitatively investigate the regular and chaotic regions in the phase space of the Dicke model.
  • To explore the correlation between classical and quantum measures of chaos.

Main Methods:

  • Utilizing efficient diagonalization techniques for a detailed quantitative study.
  • Analyzing phase space regions within the simplest nonintegrable atom-field system.

Main Results:

  • A close correlation was found between classical Lyapunov exponents and the quantum Participation Ratio of coherent states.
  • The Participation Ratio exhibits distinct scaling behaviors in regular and chaotic regimes.

Conclusions:

  • The study establishes a quantitative link between classical and quantum chaos indicators in the Dicke model.
  • The scaling properties of the Participation Ratio provide insights into the nature of regularity and chaos.