Second-Order Coherence Across the Brillouin Lasing Threshold

TL;DR

This study investigates the quantum optical properties of Brillouin scattering in a silica microsphere resonator, revealing a transition from thermal to coherent light and uncovering super-thermal statistics near the lasing threshold.

Contribution

It introduces quantum optical techniques to characterize second-order coherence in Brillouin scattering, highlighting nonlinear effects and instabilities not captured by linear models.

Findings

Transition from thermal to coherent light statistics across the threshold

Observation of super-thermal statistics near the lasing threshold

Agreement with nonlinear Langevin equation simulations

Abstract

Brillouin-Mandelstam scattering is one of the most accessible nonlinear optical phenomena and has been widely studied since its theoretical discovery one hundred years ago. The scattering mechanism is a three-wave-mixing process between two optical fields and one acoustic field and has found a broad range of applications spanning microscopy to ultra-narrow-linewidth lasers. Building on the success of utilizing this nonlinearity at a classical level, a rich avenue is now being opened to explore Brillouin scattering within the paradigm of quantum optics. Here, we take a key step in this direction by employing quantum optical techniques yet to be utilized for Brillouin scattering to characterize the second-order coherence of Stokes scattering across the Brillouin lasing threshold. We use a silica microsphere resonator and single-photon counters to observe the expected transition from bunched statistics of thermal light below the lasing threshold to Poissonian statistics of coherent light above the threshold. Notably, at powers approaching the lasing threshold, we also observe super-thermal statistics, which arise due to instability and a "flickering" in and out of lasing as the pump field is transiently depleted. The statistics observed across the transition, including the "flickering", are a result of the full nonlinear three-wave-mixing process and cannot be captured by a linearized model. These measurements are in good agreement with numerical solutions of the three-wave Langevin equations and are well demarcated by analytical expressions for the instability and the lasing thresholds. These results demonstrate that applying second-order-coherence and photon-counting measurements to Brillouin scattering provides new methods to advance our understanding of Brillouin scattering itself and progress toward quantum-state preparation and characterization of acoustic modes.