Coherence-Assisted Superradiant Laser with Hz Linewidth and $10^{-10}$W Power

The superradiant laser, based on the clock transition between the electric ground state $^1$S$_0$ and the metastable state $^3$P$_0$ of fermionic alkaline-earth(-like) atoms, has been proposed to be a new promising light source with linewidth being the order of millihertz. However, due to the small $^1$S$_0$-to-$^3$P$_0$ transition strength, the steady-state power in that system is relatively low ($\sim 10^{-12}$W). In this work, we propose an alternative superradiant laser scheme based on a Raman-transition-induced coupling between the $^3$P$_0$ and $^3$P$_1$ states in bosonic alkaline-earth(-like) atoms, and achieve a laser with linewidth $\lesssim 2\pi\times1$Hz and power $\gtrsim 10^{-10}$W ($\sim 10^{3}$ photons in steady state) at a small pumping cost. The Raman beams play two significant roles in our scheme. First, the coherence between the dark and bright states induced by the Raman beams produce a new local minimum in the pumping-linewidth curve with pumping rate lower than $2\pi \times 10$kHz, which is beneficial for continuous output. Second, the Raman beams mix the long-lived $^3$P$_0$ state into the lasing state and thus reduce the linewidth. Our work greatly improves the output performance of the superradiant laser system with coherence induced by Raman transitions and may offer a firm foundation for its practical use in future.