Analytical formulation of quantum interference inside coupled waveguides with unequal losses.

Area of Science:

• Quantum optics
• Waveguide theory
• Theoretical physics

Background:

• Quantum interference is crucial in coupled waveguide systems.
• Unequal losses in waveguides complicate theoretical modeling.
• Existing models may not fully capture quantum dynamics under lossy conditions.

Purpose of the Study:

• To develop a theoretical framework for quantum interference in coupled waveguides with unequal losses.
• To provide an analytical solution for quantum dynamics in such systems.
• To demonstrate the framework's applicability to complex waveguide configurations.

Main Methods:

• Augmenting the quantum coupled mode equation with Langevin noise terms.
• Solving the modified equation analytically.
• Deriving a closed-form formula for the Langevin noise correlation matrix.
• Utilizing the density matrix to represent the propagation state.

Main Results:

• An analytical solution for quantum interference in coupled waveguides with unequal losses was derived.
• A closed-form formula for the Langevin noise correlation matrix was obtained.
• The theoretical framework was validated using a three-waveguide anti-parity-time (PT) symmetric system.
• The framework's applicability was further demonstrated with an 89-waveguide system.

Conclusions:

• The proposed theoretical framework is self-consistent and effective for modeling quantum interference in lossy coupled waveguides.
• The analytical solution provides a comprehensive description of the propagation state's density matrix.
• The theory is applicable to a wide range of complex waveguide systems, including PT-symmetric configurations.