[Paper Review] Toward collective chemistry by strong light-matter coupling

Bing Gu|arXiv (Cornell University)|Jun 15, 2023

Strong Light-Matter Interactions4 citations

TL;DR

This paper presents an exact non-equilibrium Green's function framework for collective strong light-matter coupling in molecular ensembles, mapping molecular Hamiltonians to a coupled fermion-boson model via pseudoparticles. It enables exact computation of polaritonic dynamics in the thermodynamic limit, with finite-N corrections via diagrammatic analysis, and achieves exact agreement with numerically exact results for the driven Tavis-Cummings model, including effects of disorder and photon leakage.

ABSTRACT

Strong light-matter coupling provides a versatile and novel means to manipulate chemical processes. Here we develop a theoretical framework to investigate the spectroscopy and dynamics of a molecular ensemble embedded in an optical cavity under the collective strong coupling regime. This theory is constructed by a pseudoparticle representation of the molecular Hamiltonians, mapping the polaritonic Hamiltonian into a coupled fermion-boson model under particle number constraints. The mapped model is then analyzed using the non-equilibrium Green function theory with the important self-energy diagrams identified through power counting. Numerical demonstrations are shown for the driven Tavis-Cummings model, which shows an excellent agreement with exact results.

Motivation & Objective

• To develop a general, exact theoretical framework for studying collective strong light-matter coupling in molecular ensembles.
• To overcome the limitations of mean-field and Born-Oppenheimer approximations in many-molecule polaritonic systems.
• To systematically include finite-N corrections, disorder, photon leakage, and non-adiabatic effects in polaritonic dynamics.
• To provide a unified approach applicable to diverse molecular Hamiltonians, including those with conical intersections and vibrational modes.
• To establish a rigorous theoretical foundation for understanding cavity-altered chemistry in the collective strong coupling regime.

Proposed method

• Introduce a pseudoparticle representation that maps each molecular eigenstate to a single-particle orbital, transforming the many-body Hamiltonian into a coupled fermion-boson model.
• Apply non-equilibrium Green's function theory to the mapped model, using bare Green's functions and self-energy diagrams for perturbative expansion.
• Use power counting to classify Feynman diagrams by their scaling with N, identifying only N⁰ diagrams as relevant in the thermodynamic limit.
• Derive the Dyson equation for the photon Green's function, with the polarization function Π(ω) capturing collective effects via the sum over molecular transitions.
• Incorporate disorder by averaging over a distribution of transition frequencies, leading to a modified polarization function involving the imaginary error function.
• Account for photon leakage and decay through the imaginary part of the cavity frequency in the photon Green's function.

Experimental results

Research questions

• RQ1 Under what conditions does collective strong light-matter coupling induce measurable changes in chemical processes?
• RQ2 How do dark states and disorder affect the stability and splitting of polaritonic states in molecular ensembles?
• RQ3 Can a unified theoretical framework describe both photochemical and ground-state chemistry under collective strong coupling?
• RQ4 How do finite-size effects and many-body correlations modify the Rabi splitting in large molecular ensembles?
• RQ5 What is the role of collective polarization in sustaining coherent dynamics in the presence of decoherence and disorder?

Key findings

• The theory achieves exact agreement with numerically exact results for the driven Tavis-Cummings model, validating its accuracy in the thermodynamic limit.
• Rabi splitting arises from collective polarization of all molecules, scaling with √N, and is highly sensitive to energetic disorder.
• In the presence of disorder, Rabi splitting first increases with inhomogeneous broadening σ when σ ≪ λ, then decreases when σ ≈ λ, and vanishes when σ ≫ λ.
• The polarization function for disordered systems is expressed using the imaginary error function, capturing the non-monotonic dependence of splitting on disorder strength.
• Dark states acquire photonic fractions when disorder is significant, leading to a central peak in the photon Green's function at the molecular transition frequency.
• Finite-N corrections are systematically included via higher-order diagrams in the self-energy, with the Hartree diagram being the leading-order contribution in the N⁰ class.