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In cavity optomechanics, nonlinear interactions between an optical field anda mechanical resonator mode enable a variety of unique effects in classical andquantum measurement and information processing. Here, we describe nonlinearoptomechanical coupling in the membrane-in-the-middle (MIM) setup in a way thatallows direct comparison to the intrinsic optomechanical nonlinearity in astandard, single-cavity optomechanical system. We find that the enhancement ofnonlinear optomechanical coupling in the MIM system as predicted by Ludwig etal. arXiv:1202.0532 is limited to the degree of sideband resolution of thesystem. Moreover, we show that the selectivity of the MIM system of nonlinearover linear transduction has the same limit as in a single cavity system. Thesefindings put constraints on the experiments in which it is advantageous to usea MIM system. We discuss dynamical backaction effects in this system and findthat these effects per cavity photon are exactly as strong as in a singlecavity system, while allowing for reduction of the required input power. Wepropose using the nonlinear enhancement and reduced input power in realisticMIM systems towards parametric squeezing and heralding of phonon pairs, andevaluate the limits to the magnitude of both effects.

Comparing nonlinear optomechanical coupling in membrane-in-the-middle and single-cavity optomechanical systems