Transitions as the Native Objects of Dispersive Light-Matter Dynamics

TL;DR

The paper proposes a novel framework that treats light-matter transitions as fundamental dynamical objects, simplifying the analysis of multiphoton processes and high-order Hamiltonians in quantum optics.

Contribution

It introduces a transition-based approach to analyze dispersive light-matter interactions, unifying resonant and dispersive regimes with transparent derivations.

Findings

Reveals a photon-number-independent intrinsic Rabi frequency in the Jaynes-Cummings model.

Shows persistent polaritonic hybridization in the dispersive regime.

Provides a diagrammatic method for resonant and off-resonant pathways.

Abstract

We introduce a framework where light-matter transitions, rather than states, are the primary dynamical objects. Successive compositions of elementary transitions yield multiphoton processes with compact diagrammatic bookkeeping of resonant and off-resonant pathways. This approach enables transparent derivations of effective high-order Hamiltonians in the dispersive regime, foundational to quantum-information applications. Applied to the paradigmatic Jaynes-Cummings model, our framework reveals a photon-number-independent intrinsic Rabi frequency and persistent polaritonic hybridization in the dispersive regime, unifying resonant and dispersive limits.