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

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.