Prospects for a bad cavity laser using a large ion crystal

We propose to build a bad cavity laser using forbidden transitions in large ensembles of cold ions that form a Coulomb crystal in a linear Paul trap. This laser might realize an active optical frequency standard able to serve as a local oscillator in next-generation optical clock schemes. In passive optical clocks, large ensembles of ions appear less promising, as they suffer from inhomogeneous broadening due to quadrupole interactions and micromotion-relates shifts. In bad cavity lasers however, the radiating dipoles can synchronize and generate stable and narrow-linewidth radiation. Furthermore, for specific ions, micromotion-induced shifts can be largely suppressed by operating the ion trap at a magic frequency. We discuss the output radiation properties and perform quantitative estimations for lasing on the ${^3D_2} \rightarrow {^1S_0}$ transition in ${\rm ^{176}Lu^+}$ ions in a spherically-symmetric trap.