  The coupling of laser light to a mechanical oscillator via radiation pressure
leads to the emergence of quantum mechanical correlations between the amplitude
and phase quadrature of the laser beam. These correlations form a generic
non-classical resource which can be employed for quantum-enhanced force
metrology, and give rise to ponderomotive squeezing in the limit of strong
correlations. To date, this resource has only been observed in a handful of
cryogenic cavity optomechanical experiments. Here, we demonstrate the ability
to efficiently resolve optomechanical quantum correlations imprinted on an
optical laser field interacting with a room temperature nanomechanical
oscillator. Direct measurement of the optical field in a detuned homodyne
detector ("variational measurement") at frequencies far from the resonance
frequency of the oscillator reveal quantum correlations at the few percent
level. We demonstrate how the absolute visibility of these correlations can be
used for a quantum-enhanced estimation of the quantum back-action force acting
on the oscillator, and provides for an enhancement in the relative
signal-to-noise ratio for the estimation of an off-resonant external force,
even at room temperature.

Quantum Physics;Mesoscale and Nanoscale Physics;Optics