Levitated magnetomechanical and optomechanical systems as ultra-sensitive resonators

Timberlake, Christopher (2020) Levitated magnetomechanical and optomechanical systems as ultra-sensitive resonators. University of Southampton, Doctoral Thesis, 138pp.

Record type: Thesis (Doctoral)

Abstract

Levitated resonators are versatile systems which are extremely well isolated from their environments; unlike other conventional resonators they are not restricted by energy dissipation by being mechanically tethered to a structure. Such well isolated resonators can be used to test fundamental physics, such as testing the validity of spontaneous collapse models, or exploring the limits of Newtonian gravity on the short range scale. In this thesis, two levitated systems are presented, one based on magnetic levitation with superconductors and one using the optical gradient force to trap dielectric nanoparticles. For the magnetic levitation, permanent neodymium magnets are suspended above and inside superconducting lead traps. Magnets ranging from 30 µm radius to 0.5 mm radius are stably trapped in vacuum conditions (< 10^-6 mbar), and behave as damped driven harmonic oscillators. For a 0.5 mm radius magnet sphere trapped above a superconducting lead disk, which is cooled to 5 K, we find a quality factor Q = 5500 1300 at the oscillation frequency ω₀/2π = 19.4 Hz. This corresponds to an acceleration sensitivity of S_aa^1/2 = 1.2 ± 0.2 × 10^-10 g/√Hz, for a thermal noise limited system. Such sensitivities are suitable for devising experiments to measure the gravitational interaction between record low source masses, and further sensitivity improvements are predicted with realistic experimental improvements.
For 30 µm radius magnet spheres, trapped inside a lead superconducting well, we find quality factors of up to Q = 10⁷ when cooled to 4.2 K in a liquid helium transport dewar. By transferring this setup to a 300 mK sorption refrigerator, we also find stable levitation at low pressures and temperatures, with the ability to perform feedback cooling on resonant modes. Quality factors beyond Q = 10⁷ are anticipated to be possible in this experiment, which with suitable vibration isolation will be able to test the Continuous-Spontaneous Localization (CSL) model in previously unexplored regimes.
Optical levitation of dielectric particles is also demonstrated, with silica nanosphere strapped with the gradient force by focusing a 1550 nm to a diffraction limited spot with a parabolic mirror. Fano-like anti-resonance was shown in the dynamics of the trapped particle by applying an electrostatic force when trapped at low pressure (~10^-5 mbar) with the nanoparticle charged. We speculate that a noise due to the Coulomb interaction is responsible for the asymmetric line shape, although the exact origin of this noise is unknown. The stronger the Coulomb force, the more asymmetric the lineshape, meaning we could use the strength of the Fano asymmetry parameter to characterise the magnitude of static forces on the trapped particle. This opens up the possibility of using the amount of asymmetry in the lineshape to measure static forces which affect the particle motion, but are otherwise difficult to see as they can not be "switched off" to compare to zero applied force. The minimum detected Coulomb force was 2.7 ± 0.5 × 10^-15 N, measured over one second, which was easily distinguishable from zero applied force. Smaller forces are in principle possible to measure with the current system, with further improvements predicted by reducing the vacuum pressure and recording for longer times. Such a static sensor could be used to measure short range interactions, such as the Casimir force, or for sensitive gravity detection.