Topological Amplification in Photonic Lattices

Area of Science:

• Photonics
• Condensed Matter Physics
• Topological Materials

Background:

• Topological phases offer unique properties for robust information processing.
• Non-Hermitian systems, crucial for open quantum systems, present challenges in topological characterization.
• Photonic lattices provide a versatile platform for exploring novel topological phenomena.

Purpose of the Study:

• To establish a formal equivalence for characterizing topological phases in non-Hermitian photonic lattices.
• To explore the connection between topological insulators and directional amplifiers.
• To investigate the stability and robustness of topological amplification in photonic systems.

Main Methods:

• Formal equivalence between singular value decomposition (SVD) of non-Hermitian coupling matrices and effective Hamiltonian diagonalization.
• Mapping photonic cavity arrays to an AIII topological insulator model.
• Numerical simulations to assess stability and robustness against disorder.

Main Results:

• Unveiled a theoretical framework linking SVD to topological phase characterization.
• Demonstrated a relationship between topological insulators and directional amplifiers.
• Proved the existence of stable, topologically nontrivial steady-state phases.
• Showcased the robustness of topological amplification against lattice parameter disorder.

Conclusions:

• The established theory provides a new method for analyzing topological phases in non-Hermitian photonics.
• Topological amplification in photonic lattices is a stable and disorder-robust phenomenon.
• This research bridges fundamental condensed matter concepts with practical photonic device applications.