Linear cooling of a levitated micromagnetic cylinder by vibration

We report feedback cooling of translational and librational degrees of freedom of a levitated m icromagnet cylinder, utilizing a piezoelectric actuator to apply linear feedback to high-Q mechanical modes. The normal modes are measured with a superconducting pick-up coil coupled to a dc SQUID, and phase information is fed back to the piezoelectric actuator to feedback cool a center-of-mass mode to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>∼</a:mo><a:mn>7</a:mn><a:mspace width="0.16em"/><a:mi mathvariant="normal">K</a:mi></a:mrow></a:math>, and a librational mode to <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>830</d:mn><d:mo>±</d:mo><d:mn>200</d:mn><d:mspace width="0.16em"/><d:mi>mK</d:mi></d:mrow></d:math>. Q-factors of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mn>1.0</f:mn><f:mo>×</f:mo><f:msup><f:mn>10</f:mn><f:mn>7</f:mn></f:msup></f:mrow></f:math> are evaluated for the center-of-mass mode. We find that it is plausible to achieve ground state cooling of the center-of-mass mode by introducing vibration isolation, optimizing the geometry of the pick-up coil to focus on the specific mode of interest and utilizing a state-of-the-art SQUID for detection. Published by the American Physical Society 2024