| Summary: | Measurement and feedback control of thermomechanical motion in a micromechanical resonator has been actively studied to achieve extremely high sensing performance by controlling the stochastic thermal noise. Although linear measurement-feedback control in the phase space results in the feedback cooling, extending them to the nonlinear regime, i.e., utilizing quadratic of higher-order dynamic variables in both measurement and control, can further functionalize its operations. Here, we demonstrate fully quadratic measurement-feedback protocol in a micromechanical resonator by driving the second-order nonlinearity and directly measuring quadratic variables referred as Schwinger angular momentum. Our measurement-feedback protocol enables us to achieve a noise reduction at the level of −5.1±0.2 dB over the –3-dB limitation in the continuous parametric driving. We unveil that this strong noise reduction originates in the effective cooling effect by investigating entropy production rates. These results would be further extended to investigating general performance of nonlinear information thermodynamic machines, in which the higher-order moments (e.g., variance and correlations) can be controlled with avoiding the nonlinear instability, thanks to the existence of information flows.
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