Achieving cavity-optomechanical strong coupling with high-frequency phonons provides a rich avenue for quantum technology development including quantum state-transfer, memory, and transduction, as well as enabling several fundamental studies of macroscopic phononic degrees-of-freedom. Reaching such coupling with GHz mechanical modes however has proved challenging, with a prominent hindrance being material- and surface-induced-optical absorption in many materials. Here, we circumvent these challenges and report the observation of optomechanical strong coupling to a high frequency (11 GHz) mechanical mode of a fused-silica whispering-gallery microresonator via the electrostrictive Brillouin interaction. Using an optical heterodyne detection scheme, the anti-Stokes light backscattered from the resonator is measured and normal-mode splitting and an avoided crossing are observed in the recorded spectra, providing unambiguous signatures of strong coupling. The optomechanical coupling rate reaches values as high as $G/2pi = 39 text{MHz}$ through the use of an auxiliary pump resonance, where the coupling dominates both the optical ($kappa/2pi = 3 text{MHz}$) and the mechanical ($gamma_text{m}/2pi = 21 text{MHz}$) amplitude decay rates. Our findings provide a promising new approach for optical quantum control using light and sound.
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