Towards a Precision Measurement of the Newtonian Constant of Gravitation and Accelerometry with a Levitated Microsphere in a Magneto-Gravitational Trap

Since the theory of gravity was published by Issac Newton in the seventeenth century, scientists have studied its strength, originally for the purpose of astronomy and measuring the density of the Earth. After centuries of research and measurements, \textit{G} remains the least precisely known fundamental constant. A new method for a time-of-swing measurement of \textit{G}, developed a the National Bureau of Standards 1930, is proposed using a levitated microsphere in a magneto-gravitational trap. A new magneto-gravitational trap based on a previous system from our laboratory has been developed for a measurement of \textit{G}. This trap has been designed to load large particles with low oscillation frequencies with large amplitudes of motion to improve sensitivity to \textit{G}. Because of the weak trap, a loading method has been developed utilizing electric fields to help balance the force of gravity. A stable and variable high voltage reference has been developed to provide the necessary electric field. Camera-based feedback control has been implemented for cooling the center-of-mass motion or heating the motion in a controlled way. To limit errors due to equilibrium shifts of the particle in the trap from tilt, a simple modification was made to an optical table to actively stabilize the tilt. A measurement of \textit{G} requires high sensitivity to accelerations and forces. The parameters achieved towards the measurement of \textit{G} makes this system sensitive to acceleration. The first direct use of a room temperature levitated optomechanical system as an accelerometer has been achieved, with the best sensitivity to accelerations of any room temperature levitated optomechanical system. The sensitivity was measured to be $\SI{3.6e-8}{g/\sqrt{Hz}}$