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Quantum optomechanics offers the potential to investigate quantum effects inmacroscopic quantum systems in extremely well controlled experiments. In thispaper we discuss one such situation, the dynamic stabilization of a mechanicalsystem such as an inverted pendulum. The specific example that we study is a"membrane in the middle" mechanical oscillator coupled to a cavity field via aquadratic optomechanical interaction, with cavity damping the dominant sourceof dissipation. We show that the mechanical oscillator can be dynamicallystabilized by a temporal modulation of the radiation pressure force. Weinvestigate the system both in the classical and quantum regimes highlightingsimilarities and differences.

Dynamic stabilization of an optomechanical oscillator