  Dissipative optomechanics studies the coupling of the motion of an optical
element to the decay rate of a cavity. We propose and theoretically explore a
realization of this system in the optical domain, using a combined
Michelson--Sagnac interferometer, which enables a strong and tunable
dissipative coupling. Quantum interference in such a setup results in the
suppression of the lower motional sideband, leading to strongly enhanced
cooling in the non-sideband-resolved regime. With state-of-the-art parameters,
ground-state cooling and low-power quantum-limited position transduction are
both possible. The possibility of a strong and tunable dissipative coupling
opens up a new route towards observation of fundamental optomechanical effects
such as ponderomotive squeezing or nonlinear dynamics. Beyond optomechanics,
the method suggested here can be readily transferred to other setups involving
such systems as nonlinear media, atomic ensembles, or single atoms.
