  In quantum mechanics, measurement can be used to prepare a quantum state.
This principle is applicable even for macroscopic objects, which may enable us
to see classical-quantum transition. Here, we demonstrate conditional
mechanical squeezing of a mg-scale suspended mirror (i.e. the center-of-mass
mode of a pendulum) near quantum regimes, through continuous linear position
measurement and quantum state prediction. The experiment involved the pendulum
interacting with photon coherent fields in a detuned optical cavity, which
creates an optical spring. Futhermore, the detuned cavity allows us to perform
linear position measurement by direct photo-detection of the reflected light.
We experimentally verify the conditional squeezing using the theory combining
prediction and retrodiction based on the causal and anti-causal filters. As a
result, the standard deviation of position and momentum are respectively given
by 36 times the zero-point amplitude of position $q_{\rm zpf}$ and 89 times the
zero-point amplitude of momentum $p_{\rm zpf}$. The squeezing level achieved is
about 5 times closer to the zero-point motion, despite that the mass of the
mechanical oscillator is approximately 7 orders of magnitude greater, compared
to the previous study. Thus, our demonstration is the first step towards
quantum control for massive objects whose mass-scale is high enough to measure
gravitational interactions. Such quantum control will pave the way to test
quantum mechanics using the center-of-mass mode of massive objects.
