  Brillouin-based optomechanical systems with high-frequency acoustic modes
provide a promising platform for implementing quantum-information processing
and wavelength conversion applications, and for probing macroscopic quantum
effects. Achieving strong coupling through electrostrictive Brillouin
interaction is essential for coupling the massive mechanical mode to an optical
field, thereby controlling and characterizing the mechanical state. However,
achieving strong coupling at room temperature has proven challenging due to
fast mechanical decay rates, which increase the pumping power required to
surpass the coupling threshold. Here, we report an optomechanical system with
independent control over pumping power and frequency detuning to achieve and
characterize the strong-coupling regime of a bulk acoustic-wave resonator.
Through spectral analysis of the cavity reflectivity, we identify clear
signatures of strong coupling, i.e., normal-mode splitting and an avoided
crossing in the detuned spectra, while estimating the mechanical linewidth
$\Gamma_m/2\pi~=~7.13MHz$ and the single-photon coupling rate
$g_0/2\pi~=~7.76Hz$ of our system. Our results provide valuable insights into
the performances of room-temperature macroscopic mechanical systems and their
applications in hybrid quantum devices.
