  We propose a versatile, free-space cavity optomechanics platform built from
two photonic crystal membranes, one of which is freely suspended, and designed
to form a microcavity less than one wavelength long. This cavity features a
series of photonic bound states in the continuum that, in principle, trap light
forever and can be favorably used together with evanescent coupling for
realizing various types of optomechanical couplings, such as linear or
quadratic coupling of either dispersive or dissipative type, by tuning the
photonic crystal patterning and cavity length. Crucially, this platform allows
for a quantum cooperativity exceeding unity in the ultrastrong single-photon
coupling regime, surpassing the performance of conventional Fabry-Perot-based
cavity optomechanical devices in the non-resolved sideband regime. This
conceptually novel platform allows for exploring new regimes of the
optomechanical interaction, in particular in the framework of pulsed and
single-photon optomechanics.
