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arXiv:2310.05763 · Physical Review A

Bayesian inference for near-field interferometric tests of collapse models

Shaun Laing, James Bateman

Published Jul 12, 2024• 2 citations
arXivHTMLPDF

Abstract

We explore the information which proposed matterwave interferometry experiments with large test masses can provide about parameterizable extensions to quantum mechanics, such as have been proposed to explain the apparent quantum to classical transition. Specifically, we consider a matterwave near-field Talbot interferometer and Continuous Spontaneous Localization (CSL). Using Bayesian inference we compute the effect of decoherence mechanisms including pressure and blackbody radiation, find estimates for the number of measurements required, and provide a procedure for optimal choice of experimental control variables. We show that in a simulated space-based experiment it is possible to reach masses of ∼ 10 9 u , and we quantify the bounds which can be placed on CSL. These specific results can be used to inform experimental design, and the general approach can be applied to other parameterizable models. Published by the American Physical Society 2024

DOI
10.1103/physreva.110.012214

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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.
The transition from the quantum to the classical realm remains one of the most profound open questions in physics. While quantum theory predicts the existence of macroscopic superpositions, their apparent absence in the everyday world is attributed either to environmental decoherence or to an intrinsic mechanism for wave-function collapse. This work presents a quantitative and experimentally grounded framework for distinguishing these possibilities. We propose a levitated optomechanical platform capable of generating controllable Schrodinger-cat states in the center of mass motion of a dielectric nanosphere. A comprehensive master equation incorporates gas collisions, black-body radiation, and photon-recoil noise, establishing a calibrated environmental baseline. The Continuous Spontaneous Localization (CSL) model is embedded within the same framework, predicting a characteristic saturation of the decoherence rate with superposition size and a quadratic scaling with mass. A Bayesian inference protocol is outlined to discriminate collapse induced excess decoherence from environmental noise. Together these elements provide a concrete experimental blueprint for a decisive test of quantum linearity, either revealing new physics beyond standard quantum mechanics or setting the most stringent bounds to date on objective-collapse parameters.
Wave function collapse models postulate a fundamental breakdown of the quantum superposition principle at the macroscale. Therefore, experimental tests of collapse models are also fundamental tests of quantum mechanics. Here, we compute the upper bounds on the collapse parameters, which can be inferred by the gravitational wave detectors LIGO, LISA Pathfinder, and AURIGA. We consider the most widely used collapse model, the continuous spontaneous localization (CSL) model. We show that these experiments exclude a huge portion of the CSL parameter space, the strongest bound being set by the recently launched space mission LISA Pathfinder. We also rule out a proposal for quantum-gravity-induced decoherence.
The model of continuous spontaneous localization (CSL) is the most prominent consistent modification of quantum mechanics predicting an objective quantum-to-classical transition. Here we show that precision interferometry with Bose-Einstein-condensed atoms can serve to lower the current empirical bound on the localization rate parameter by several orders of magnitude. This works by focusing on the atom count distributions rather than just mean population imbalances in the interferometric signal of squeezed Bose-Einstein condendates, without the need for highly entangled Greenberger-Horne-Zeilinger-like states. In fact, the interplay between CSL-induced diffusion and dispersive atom-atom interactions results in an amplified sensitivity of the condensate to CSL. We discuss experimentally realistic measurement schemes utilizing state-of-the-art experimental techniques to test new regions of parameter space and, pushed to the limit, to probe and potentially rule out large relevant parameter regimes of CSL.
Abstract Models of spontaneous wave function collapse describe the quantum-to-classical transition by assuming a progressive breakdown of the superposition principle when the mass of the system increases, providing a well-defined phenomenology in terms of a non-linearly and stochastically modified Schrödinger equation, which can be tested experimentally. The most popular of such models is the continuous spontaneous localization (CSL) model: in its original version, the collapse is driven by a white noise, and more recently, generalizations in terms of colored noises, which are more realistic, have been formulated. We will analyze how current non-interferometric tests bound the model, depending on the spectrum of the noise. We will find that low frequency purely mechanical experiments provide the most stable and strongest bounds. Graphical abstract