# Prospects for a bad cavity laser using a large ion crystal

## TL;DR

This paper explores the potential of a bad cavity laser using large ion crystals in a linear trap, aiming to develop highly stable optical frequency standards for advanced clock systems.

## Contribution

It proposes a novel approach to build a bad cavity laser with large ion ensembles, addressing inhomogeneous broadening issues and suggesting methods to suppress shifts for improved stability.

## Key findings

- Potential for stable, narrow-linewidth laser radiation.
- Feasibility of using ${^{176}Lu^+}$ ions in a spherical trap.
- Strategies to mitigate micromotion-induced shifts.

## Abstract

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.