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We realise a feedback-controlled optical Fabry-Perot cavity in which thetransmitted cavity output is used to modulate the input amplitude fluctuations.The resulting phase-dependent fluctuations of the in-loop optical field, whichmay be either sub-shot- or super-shot-noise, can be engineered to favorablyaffect the optomechanical interaction with a nanomechanical membrane placedwithin the cavity. Here we show that in the super-shot-noise regime("anti-squashed light") the in-loop field has a strongly reduced effectivecavity linewidth, corresponding to an increased optomechanical cooperativity.In this regime feedback improves the simultaneous resolved sideband cooling oftwo nearly degenerate membrane mechanical modes by one order of magnitude.

Enhancement of three-mode optomechanical interaction by feedback-controlled light