  We demonstrate 8.5 dB thermal squeezing of a membrane oscillator using the
dynamical backaction effect and electrostatic feedback in an optomechanical
membrane-in-the-middle setup. We show that strong squeezing can be obtained
even in the far detuning regime of a sideband-resolved system. By using the
dielectrophoretic force of a metallic needle kept in close proximity to the
membrane, we implement the one-quadrature active feedback scheme to prevent the
divergence of the amplified quadrature and surpass the 3 dB limit of mechanical
squeezing. We also discuss different regions of the sideband spectrum where
strong squeezing can be obtained. Although the demonstration here is classical,
this technique is equally applicable to prepare the mechanical oscillator in a
quantum squeezed state.
