Approaching the Quantum Limit of Position Measurements in a Magneto-Gravitational Trap*

Levitated particles in vacuum hold promise for tests of fundamental physics due to their isolation from the environment and easily controlled simple harmonic motion. The static trapping fields of magneto-gravitational traps, which use the repulsion of diamagnetic materials by magnetic fields combined with Earth's gravity, are particularly well-suited to precision measurements. Furthermore, the relatively large possible mass of levitated particles and the weak restoring force in these traps makes them attractive for gravitational measurements and macroscopic tests of quantum mechanics. Our measurements in these traps begin with precision tracking of the particle position. We present a method of tracking the position of a trapped microsphere with precision near the shot noise limit, even with large microspheres and millimeter-scale displacements, using CMOS cameras and a novel image analysis algorithm. This method enables nearly shot noise limited detection of microsphere motion for a potential new measurement of the Newtonian constant of gravitation as well as position measurements approaching the standard quantum limit in the quasi-free particle regime.