  Steady-state superradiance and superradiant lasing attract significant
attentions in the field of optical lattice clocks, but have not been achieved
so far due to the technical challenges and atom loss problem. In this article,
we propose that their counter-part may be observed in the microwave domain with
solid-state spins-microwave resonator systems at room temperature with
realistic technical restrictions. To validate our proposal, we investigate
systematically the system dynamics and steady-state by solving quantum master
equations for the multi-level and multi-process dynamic of trillions of spins.
To this end, we employ a mean-field approach, and convert the mean-field
dynamics of the spin ensemble into the one in a more intuitive Dicke state
picture. Our calculations show that for systems with nitrogen vacancy center
spins and pentacene molecular spins the superradiant Rabi oscillations occur
firstly due to transitions among different Dicke states, and the subsequent
continuous-wave superradiant masing can achieve a linewidth well below
millihertz. Our work may guide further exploration of transient and
steady-state superradiant masing with the mentioned and other solid-state spins
systems, such as silicon vacancy centers in silicon carbide and boron vacancy
centers in hexagonal boron nitride, where the coherent radiation with
ultra-narrow linewidth may find applications in deep-space communications,
radio astronomy and high-precision metrology.
