Preparing mechanical squeezing of a macroscopic pendulum near quantum regimes

We present the mechanical squeezing of a mg-scale suspended mirror (i.e. a pendulum) near quantum regimes through continuous linear position measurement. The experiment involved the pendulum interacting with photon coherent fields in a detuned optical cavity. The position uncertainty in the measured data is reduced and squeezed to $470$ times the zero-point amplitude $x_{\rm zpf}$ with a purity of about 0.0004, by means of optimal state estimation through causal Wiener filtering. The purity of the squeezed state is clearly maximized by the Wiener filter, based on precisely identified optomechanical parameters. This is the first step for measurement-based quantum control of macroscopic pendulums, e.g. generation of an entanglement state between macroscopic pendulums. Such quantum control will provide a direct insight into the quantum to classical transition and will pave the way to test semiclassical gravity and gravity sourced by macroscopic quantum oscillators.Comment: 6 pages, 3figures, and a supplemental materia