Towards a Precise Measurement of the Newtonian Constant of Gravitation Using Levitated Optomechanics

The Newtonian gravitational constant, G, remains the least precisely known fundamental constant in physics, with a standard uncertainty of 22 ppm. Our experiment uses a time-of-swing method, but instead of a pendulum, we levitate millimeter-scale diamagnetic graphite rods in a linear quadrupole magneto-gravitational trap under ultra-high vacuum (∼ 10−9 Torr). In this approach, the gravitational interaction between source masses and a levitated graphite rod shifts the particle’s oscillation frequency, from which G is determined. This levitated system reduces many limitations of traditional torsion-balance experiments but introduces new challenges, including damping from eddy currents and charge, environmental vibrations, and measurement noise. Characterizing and minimizing dissipation is therefore essential for achieving long coherence times and accurate frequency measurements. The trap design suppresses dissipation of the axial motion, allowing low-frequency oscillations critical for measuring G. Ring-down measurements show a vertical damping rate of 0.3 s−1 (Q = 800) at 39 Hz and an axial

damping rate of 2.1 × 10−6 s−1 (Q = 1.2 × 106) at 0.40 Hz, demonstrating high stability and long coherence times. To further improve sensitivity, we are implementing temperature stabilization, modifying trap potentials by shaping the magnetic field, and using inline holography to measure the particle position with higher precision. These advances aim to reduce the oscillation frequency toward 0.01 Hz and minimize measurement noise. This platform shows strong promise for high-precision determination of G and highlights levitated optomechanics as a

powerful tool for fundamental physics research.