Bayesian Inference and Collapse Models in Levitated Optomechanics - SHAUN LAING (2024)
An apparent contradiction exists between the wave nature of quantum mechanics allowing for superposition of states, and the observations of classical mechanics.Several possible solutions for this discrepancy have been suggested including the proposal that quantum and classical dynamics are simply approximations to a universal dynamics. Collapse models modify the usual Schrödinger equation that provides this universal dynamics and can be tested experimentally. In this thesis, we conceive of a Talbot matter-wave interferometer to probe the superposition of high-mass nanoparticles. We extend existing descriptions beyond the point-like regime allowing us to test collapse models with masses up to 109u. During this development, we discover and correct an error in calculating the Talbot coeﬃcients for a laser grating in the Mie regime. A Bayesian analysis is performed on simulated data making greater use of each recorded arrival position of the nanoparticle and provide a real-valued probability density to the parameter space as opposed to the binary exclusion plots of previous works. We ﬁnd a limit to the size of spherical particles that can be used as a result of the grating transformation being averaged over the particle. As a result, during a collaboration with the Geraci group at Northwestern University, we develop a numerical method for ﬁnding where arbitrarily shaped particles scatter information about their position and use these techniques to derive the Talbot coeﬃcients for arbitrary particle geometries.