  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.
