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We present an approach for exponentially enhancing the single-photon couplingstrength in an optomechanical system using only additional linear resources. Itallows one to reach the quantum nonlinear regime of optomechanics, wherenonlinear effects are observed at the single photon level, even if the barecoupling strength is much smaller than the mechanical frequency and cavitydamping rate. Our method is based on using a large amplitude, strongly detunedmechanical parametric drive to amplify mechanical zero-point fluctuations andhence enhance the radiation pressure interaction. It has the further benefit ofallowing time-dependent control, enabling pulsed schemes. For a two-cavityoptomechanical setup, we show that our scheme generates photon blockade forexperimentally accessible parameters, and even makes the production of photonicstates with negative Wigner functions possible. We discuss how our method is anexample of a more general strategy for enhancing boson-mediated two-particleinteractions and nonlinearities.

Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification