  We theoretically show that laser recoil heating in free-space levitated
optomechanics can be arbitrarily suppressed by shining squeezed light onto an
optically trapped nanoparticle. The presence of squeezing modifies the quantum
electrodynamical light-matter interaction in a way that enables us to control
the amount of information that the scattered light carries about a given
mechanical degree of freedom. Moreover, we analyze the trade-off between
measurement imprecision and back-action noise and show that optical detection
beyond the standard quantum limit can be achieved. We predict that, with
state-of-the-art squeezed light sources, laser recoil heating can be reduced by
at least 60% by squeezing a single Gaussian mode with an appropriate incidence
direction, and by 98% by squeezing a properly mode-matched mode. Our results,
which are valid both for motional and librational degrees of freedom, will lead
to improved feedback cooling schemes as well as boost the coherence time of
optically levitated nanoparticles in the quantum regime.
