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Brillouin-Mandelstam scattering is one of the most accessible nonlinearoptical phenomena and has been widely studied since its theoretical discoveryone hundred years ago. The scattering mechanism is a three-wave mixing processbetween two optical fields and one acoustic field and has found a broad rangeof applications spanning microscopy to ultra-narrow-linewidth lasers. Buildingon the success of utilizing this nonlinearity at a classical level, a richavenue is now being opened to explore Brillouin scattering within the paradigmof quantum optics. Here, we take a key step in this direction by employingquantum optical techniques yet to be utilized for Brillouin scattering tocharacterize the second-order coherence of Stokes scattering across theBrillouin lasing threshold. We use a silica microsphere resonator andsingle-photon counters to observe the expected transition from bunchedstatistics of thermal light below the lasing threshold to Poissonian statisticsof coherent light above the threshold. Notably, at powers approaching thelasing threshold, we also observe super-thermal statistics, which arise due toinstability and a ``flickering'' in and out of lasing as the pump field istransiently depleted. The statistics observed across the transition, includingthe ``flickering'', are a result of the full nonlinear three-wave mixingprocess and cannot be captured by a linearized model. These measurements are ingood agreement with numerical solutions of the three-wave Langevin equationsand are well demarcated by analytical expressions for the instability and thelasing thresholds. These results demonstrate that applyingsecond-order-coherence and photon-counting measurements to Brillouin scatteringprovides new methods to advance our understanding of Brillouin scatteringitself and progress toward quantum-state preparation and characterization ofacoustic modes.

Second-Order Coherence Across the Brillouin Lasing Threshold