Title: Bulk crystalline optomechanics,
Abstract: Brillouin processes couple light and sound through optomechanical three-wave
interactions. Within bulk solids, this coupling is mediated by the intrinsic
photo-elastic material response yielding coherent emission of high frequency
(GHz) acoustic phonons. This same interaction produces strong optical
nonlinearities that overtake both Raman or Kerr nonlinearities in practically
all solids. In this paper, we show that the strength and character of Brillouin
interactions are radically altered at low temperatures when the phonon
coherence length surpasses the system size. In this limit, the solid becomes a
coherent optomechanical system with macroscopic (cm-scale) phonon modes
possessing large ($60\ \mu \rm{g}$) motional masses. These phonon modes, which
are formed by shaping the surfaces of the crystal into a confocal phononic
resonator, yield appreciable optomechanical coupling rates (${\sim}100$ Hz),
providing access to ultra-high $Q$-factor ($4.2{\times}10^7$) phonon modes at
high ($12$ GHz) carrier frequencies. The single-pass nonlinear optical
susceptibility is enhanced from its room temperature value by more than four
orders of magnitude. Through use of bulk properties, rather than
nano-structural control, this comparatively simple approach is enticing for the
ability to engineer optomechanical coupling at high frequencies and with high
power handling. In contrast to cavity optomechanics, we show that this system
yields a unique form of dispersive symmetry breaking that enables selective
phonon heating or cooling without an optical cavity (i.e., cavity-less
optomechanics). Extending these results, practically any transparent
crystalline material can be shaped into an optomechanical system as the basis
for materials spectroscopy, new regimes of laser physics, precision metrology,
quantum information processing, and for studies of macroscopic quantum
coherence.