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Dynamical properties of two coupled quantum cavities with single-mode amplification.

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  • 1Dipartimento di Scienza Applicata e Tecnologia, <a href="https://ror.org/00bgk9508">Politecnico di Torino</a>, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.

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Summary

This study explores coupled optical cavities with amplification, revealing a complex dynamical scenario. Mode interaction creates a stable subdomain within the unstable amplification region, altering amplification effects.

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Area of Science:

  • Quantum optics
  • Theoretical physics
  • Nonlinear dynamics

Background:

  • Coupled optical cavities are fundamental for engineering bosonic mode interactions.
  • Amplification terms in optical systems can lead to complex dynamical behaviors.

Purpose of the Study:

  • To investigate a two-mode coupled optical cavity model with an amplification term.
  • To analyze the resulting dynamical scenario and stability properties.

Main Methods:

  • Utilized the dynamical-algebra method, a group-theoretic approach, for model diagonalization.
  • Determined the stability diagram of the model Hamiltonian.
  • Performed analytic studies of the energy spectrum and calculated time evolution of mode populations.

Main Results:

  • Mode interaction significantly modifies amplification, splitting the unstable domain into two subdomains.
  • One subdomain remains stable, exhibiting no amplification, with its extent controlled by interaction parameters.
  • Energy spectrum transitions from discrete to continuous at the stability boundary.

Conclusions:

  • The interplay between mode coupling and amplification leads to rich, non-trivial dynamics in optical cavities.
  • The dynamical-algebra method effectively maps stability diagrams and predicts system behavior.
  • Analytic solutions confirm the stability transitions and amplification effects.