Ultra-low damping of the translational motion of a composite graphite rod in a magneto-gravitational trap

Abstract

We demonstrate an ultra-low dissipation, one-dimensional mechanical oscillator formed by levitating a millimeter-scale composite graphite rod in a room-temperature magneto-gravitational trap. The trap's magnetic field geometry, based on a linear quadrupole, eliminates first-order field gradients in the axial direction, yielding a low oscillation frequency with ultra-low eddy-current losses. Direct ring-down measurements under vacuum compare the damping of the vertical and axial motion; while the vertical motion damps in seconds, the axial motion damps with a time constant of over 5 days. Analysis reveals that this dramatic difference in damping is a result of the symmetry of the magnetic field and the anisotropy of the trap strength. The results are remarkably robust, demonstrating a potential platform for inertial and gravitational sensing.

Figures (4)

• Figure 1: A schematic of the magneto-gravitational trap used for levitating a graphite rod. Set screws are used to adjust the height of the end-magnet stacks (each composed of three smaller NdFeB magnets) on both axial ends of the trap in order to create a low-frequency axial trapping potential. North (N) and south (S) pole labels are shown to describe the magnet orientations relative to each other. The dark cylinder in the gap between the pole pieces represents the trapped composite graphite rod.
• Figure 2: A plot of the relative transverse magnetic field, $B_x(x=0)$, near the rod's equilibrium position (shown by the red "x"). Note the difference in scale between $z$ and $y$, indicative of the high level of anisotropy in the trap. The $y$-axis is shown magnified 100 times relative to the $z$-axis.
• Figure 3: An image of a piece of ${\sim}\qty{0.5}{\milli \meter}$-diameter piece of Pentel 4B pencil lead levitated in an MGT imaged along the $x$-axis. The top and bottom black sections are the top and bottom pole pieces. The pixel size is calibrated to be 3.45 before the images undergo $4 \text{x} 4$ binning when saved.
• Figure 4: Plot (a) displays several oscillation cycles in the vertical ($y$) motion and a few cycles in the axial ($z$) motion of the levitated 4B graphite rod. Plot (b) presents the kinetic-energy fit to the rod’s $y$-motion over a 30-second interval, representative of the five data sets that show consistent behavior, and plot (c) shows the kinetic-energy fit to the rod's $z$-motion over three 24-hour data sets. The exponential fits to the energy are displayed as black lines. The vertical and axial damping rates were measured to be $\Gamma_y = \qty{0.305\pm0.001}{s^{-1}}$ and $\Gamma_z = \qty{2.1\pm0.2d-6}{s^{-1}}$. Only every tenth measured and fitted point is displayed in (c) to reduce the image size.