  Superradiant Raman scattering of Rubidium atoms has been explored in the
experiment [Nature 484, 78 (2012)] to prove the concept of the superradiant
laser, which attracts significant attentions in quantum metrology due to the
expected ultra-narrow linewidth down to millihertz. To better understand the
physics involved in this experiment, we have developed a quantum master
equation theory by treating the Rubidium atoms as three-level systems, and
coupling them with a dressed laser and an optical cavity. Our simulations show
different superradiant Raman scattering pulses for the systems within the
crossover and strong coupling regime, and the shifted and broader spectrum of
the steady-state Raman scattering. Thus, our studies provide a unified view on
the superradiant Raman scattering pulses, and an alternative explanation to the
broad spectrum of the steady-state Raman scattering, as observed in the
experiment. In future, our theory can be readily applied to study other
interesting phenomena relying on the superradiant Raman scattering, such as
magnetic field sensing, real-time tracking of quantum phase, Dicke phase
transition of non-equilibrium dynamics and so on.
