Generalization of the Einstein coefficients and rate equations under the quantum Rabi oscillation

TL;DR

This paper extends Einstein coefficients and rate equations to include quantum Rabi oscillations, providing analytical results for multimode Jaynes-Cummings models in lossy cavities with thermal and coherent photons, aligning with experimental data.

Contribution

It introduces a quantum field theoretic generalization of Einstein coefficients incorporating Rabi oscillations and derives analytical multimode Jaynes-Cummings results for complex light-matter interactions.

Findings

Analytical results match experimental data by Brune et al.

Renormalized coupling constants for different photon states.

Generalized rate equations describe population dynamics.

Abstract

We have generalized Einstein coefficients and rate equations from quantum field theoretic point of view by bringing the fundamental processes and the quantum Rabi oscillation in a single footing for the light-matter interactions for nonzero Rabi frequency. We have analytically obtained multimode Jaynes-Cummings model results for the quantum Rabi oscillations of a two-level system in a lossy resonant cavity containing (i) thermal photons and (ii) injected photons of a coherent field. We have renormalized the coupling constant for the light-matter interactions for these cases. Our results match well with the seminal experimental data obtained in this regard by Brune et al [Phys. Rev. Lett 76, 1800 (1996)]. We also have studied the population dynamics in this regard by applying the generalized Einstein rate equations.