Optimal squeezed cooling of a mechanical oscillator using measurement-based vector feedback

Measurement-based feedback has been adopted as an efficient cooling scheme capable of suppressing the thermal fluctuation of a mechanical resonator to a level limited by measurement imprecision. We present a scheme of squeezed cooling in which the limit of feedback cooling imposed by the measurement imprecision is surpassed by parametrically squeezing the mechanical resonator in a periodically oscillating optical trap. To stabilize the parametrically amplified quadrature and simultaneously optimize the cooling for the squeezed quadrature, a measurement-based vector feedback capable of independently controlling the orthogonal motional quadrature is implemented. Our experiment demonstrates that the optimal condition for the squeezed cooling closely depends on the strength of squeezing. With the ability to keep the orthogonal quadrature well decoupled, optimal squeezed cooling of the mechanical resonator under strong squeezing is achieved with the squeezed variance becoming 8.1 dB below the limit of feedback cooling and the creation of a 31.7 dB thermomechanical squeezed cooling. Although this research is conducted in the classical regime, the scheme of squeezed cooling can be naturally extended to quantum systems with the prospects of creating quantum squeezing of a room-temperature mechanical resonator and enabling displacement measurement beyond the standard quantum limit.