Cavity-modified Maxwell-Bloch equations for the vacuum Rabi splitting

We derive a set of cavity-modified Maxwell-Bloch equations for a two-level atom in a cavity driven by a coherent field from the single-atom Fokker-Planck equation in the bad-cavity limit. These equations have the same form as the Maxwell-Bloch equations for a two-level atom in free space interacting with a coherent field. The presence of a cavity is reflected in three cavity-modified parameters: decay rate gamma(eff), Rabi frequency Omega(eff), and detuning Delta(eff). We show that the cavity-modified Maxwell-Bloch equations provide an easy way to study cavity-modified spontaneous emission, cavity-induced radiative energy level shifts, and vacuum Rabi splitting.