Non-Hermitian Hamiltonians for linear and nonlinear optical response: A model for plexcitons.

Area of Science:

• Quantum Optics and Photonics
• Condensed Matter Physics
• Spectroscopy

Background:

• Polaritons, formed by light-matter coupling in cavities, alter material properties and exciton dynamics.
• Non-Hermitian Hamiltonians have described plexcitons (plasmon-exciton polaritons) and their optical response.
• Existing models successfully explain linear and third-order optical responses of plexcitons.

Purpose of the Study:

• To rigorously derive non-Hermitian Hamiltonians within the nonlinear spectroscopy response function formalism.
• To investigate the spectroscopic signatures of plexcitons, particularly near the exceptional point.
• To analyze the optical response below and above the exceptional point using double-sided Feynman diagrams.

Main Methods:

• Derivation of non-Hermitian Hamiltonians using Feshbach operators in the response function formalism.
• Application of these Hamiltonians to explore plexciton spectroscopic signatures.
• Analysis of optical response and eigenvalue symmetry changes across the exceptional point using Feynman diagrams.

Main Results:

• A clear distinction between interference and Rabi splitting in linear spectroscopy was identified.
• A qualitative change in the nonlinear signal's line shape symmetry was observed when crossing the exceptional point.
• This symmetry change in the optical response correlates with changes in the Hamiltonian's eigenvalue symmetry.

Conclusions:

• The study provides a robust framework for simulating optical responses of electronic sublevels.
• Nonlinear spectroscopy can effectively probe different spectral regimes of non-Hermitian Hamiltonians.
• The findings offer new avenues for understanding and manipulating light-matter interactions in plexcitonic systems.