# The Phonon-Limited-Linewidth of Brillouin Lasers at Cryogenic Temperatures

## TL;DR

This paper measures the fundamental linewidth of stimulated Brillouin lasers at cryogenic temperatures in silica microresonators, confirming the theory that phonon occupancy dominates linewidth and affects quantum limits.

## Contribution

It provides experimental validation of the phonon-based linewidth theory for SBLs at cryogenic temperatures, linking temperature dependence to phonon occupancy.

## Key findings

- Linewidth decreases with temperature, matching phonon occupancy predictions.
- Quantum limit of linewidth is twice the Schawlow-Townes limit due to phonon participation.
- Agreement between measured phonon occupancy and Bose-Einstein statistics supports the theory.

## Abstract

Laser linewidth is of central importance in spectroscopy, frequency metrology and all applications of lasers requiring high coherence. It is also of fundamental importance, because the Schawlow-Townes laser linewidth limit is of quantum origin. Recently, a theory of stimulated Brillouin laser (SBL) linewidth has been reported. While the SBL linewidth formula exhibits power and optical Q factor dependences that are identical to the Schawlow-Townes formula, a source of noise not present in two-level lasers, phonon occupancy of the Brillouin mechanical mode, is predicted to be the dominant SBL linewidth contribution. Moreover, the quantum-limit of the SBL linewidth is predicted to be twice the Schawlow-Townes limit on account of phonon participation. To help confirm this theory the SBL fundamental linewidth is measured at cryogenic temperatures in a silica microresonator. Its temperature dependence and the SBL linewidth theory are combined to predict the number of thermo-mechanical quanta at three temperatures. The result agrees with the Bose-Einstein phonon occupancy of the microwave-rate Brillouin mode in support of the SBL linewidth theory prediction.