Phonon lasing from optical frequency comb illumination of a trapped ion

An atomic transition can be addressed by a single tooth of an optical frequency comb if the excited state lifetime ($\tau$) is significantly longer than the pulse repetition period ($T_\mathrm{r}$). In the crossover regime between fully-resolved and unresolved comb teeth ($\tau \lessapprox T_\mathrm{r}$), we observe Doppler cooling of a pre-cooled trapped atomic ion by a single tooth of a frequency-doubled optical frequency comb. We find that for initially hot ions, a multi-tooth effect gives rise to lasing of the ion's harmonic motion in the trap, verified by acoustic injection locking. The gain saturation of this phonon laser action leads to a comb of steady-state oscillation amplitudes, allowing hot ions to be loaded directly into the trap and laser cooled to crystallization despite the presence of hundreds of blue-detuned teeth.