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

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.