  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.
