Study of the Brownian motion of a torsion pendulum induced by the eddy current with torque sensitivity of sub-femto Nm

Due to the excellent sensitivity for small torque, torsion pendulums are widely used. The thermal noise is a fundamental limit according to the fluctuation-dissipation theorem. The damping induced by the eddy current has been well studied, but it has not been verified directly whether the eddy current generates the Brownian motion in accordance with the fluctuation-dissipation theorem for a macroscopic pendulum. In this work, we verify the Brownian motion induced by the eddy current using torsion pendulums in the geomagnetic field. For a hollow cube aluminum pendulum with a side length of 50 mm and thickness of 1 mm, the measured torque noise is about 1×10-15Nm/Hz, consistent with the thermal noise predicted by the eddy current in a 60.5 μT ambient magnetic field. By applying the magnetic shield for a disk-shaped pendulum, the torque noise is improved to 1×10-16Nm/Hz and reaches the thermal noise limit with quality factor Q = 4.3 × 105.