The superradiant instability can lead to the generation of extremely dense axion clouds around rotating black holes. We show that, despite the long lifetime of the QCD axion with respect to spontaneous decay into photon pairs, stimulated decay becomes significant above a minimum axion density and leads to extremely bright lasers. The lasing threshold can be attained for axion masses $mu gtrsim 10^{-8} mathrm{eV}$, which implies superradiant instabilities around spinning primordial black holes with mass $lesssim 0.01M_odot$. Although the latter are expected to be non-rotating at formation, a population of spinning black holes may result from subsequent mergers. We further show that lasing can be quenched by Schwinger pair production, which produces a critical electron-positron plasma within the axion cloud. Lasing can nevertheless restart once annihilation lowers the plasma density sufficiently, resulting in multiple laser bursts that repeat until the black hole spins down sufficiently to quench the superradiant instability. In particular, axions with a mass $sim 10^{-5} mathrm{eV}$ and primordial black holes with mass $sim 10^{24}$ kg, which may account for all the dark matter in the Universe, lead to millisecond-bursts in the GHz radio-frequency range, with peak luminosities $sim 10^{42}$ erg/s, suggesting a possible link to the observed fast radio bursts.
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