  Squeezing light is a critical resource in both fundamental physics and
precision measurement. The squeezing light has been generated through
optical-parametric amplification inside an optical resonator. However,
preparing the squeezing light in an optomechanical system is still a challenge
for the thermal noise inevitably coupling to the system. We consider an
optically levitated nano-particle in a bichromatic cavity, in which two cavity
modes could be excited by the scattering photons of the dual-tweezers
respectively. Based on the coherent scattering mechanism, the ultra-strong
coupling between the cavity field and torsional motion of nano-particle could
be achieved for the current experimental conditions. With the back-action of
the optically levtiated nano-particle, the broad single-mode squeezing light
can be realized in the bad cavity regime. Even at room temperature, the
single-mode light can be squeezed for more than 17 dB, which is far beyond the
3 dB limit. The two-mode squeezing lights can also be generated, if the optical
tweezers contain two frequencies, one is on the red sideband of the cavity
mode, the other is on the blue sideband. The two-mode squeezing can be
maximized near the boundary of the system stable regime, and is sensitive to
both the cavity decay rate and the power of the optical tweezers.
