Non-equilibrium quadratic measurement-feedback squeezing in a micromechanical resonator

Measurement and feedback control of stochastic dynamics has been actively studied for not only stabilizing the system but also generating additional entropy flows originating in information flow controller. In particular, a micromechanical offers great platform to investigate such non-equilibrium under measurement-feedback owing its precise controllability small fluctuations. Although various types protocols have demonstrated with linear observables (e.g., displacement velocity), extending them nonlinear regime, i.e., utilizing both measurement control, retains non-trivial phenomena dynamics. Here, we demonstrate resonator by driving second-order nonlinearity (i.e., parametric squeezing) directly measuring quadratic observables, which are given Schwinger representation pseudo angular momentum (referred as momentum). contrast that divergence occurs when is blindly driven, our protocol enables us avoid achieve strong noise reduction at level $-5.1\pm 0.2$ dB. This originates effective cooling included protocol, unveiled investigating production rates coarse-grained model. Our results open up possibility improving noise-limited sensitivity performance thermodynamic machines feedback.