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.
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.
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
Matter wave interferometry with increasingly larger masses could pave the way to understanding the nature of wavefunction collapse, the quantum to classical transition, or even how an object in a spatial superposition interacts with its gravitational field. In order to improve upon the current mass record, it is necessary to move into the nanoparticle regime. In this paper, we provide a design for a nanoparticle Talbot–Lau matter wave interferometer that circumvents the practical challenges of previously proposed designs. We present numerical estimates of the expected fringe patterns that such an interferometer would produce, considering all major sources of decoherence. We discuss the practical challenges involved in building such an experiment, as well as some preliminary experimental results to illustrate the proposed measurement scheme. We show that such a design is suitable for seeing interference fringes with 106 amu SiO2 particles and that this design can be extended to even 108 amu particles by using flight times below the typical Talbot time of the system.
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.
An open problem in modern physics is why microscopic quantum objects can be at two places at once (i.e. a superposed quantum state) while macroscpoic classical object never show such a behaviour. Collapse models provides a quantitative answer for this problem and explain how macroscopic classical world emerges out of microscopic quantum world. A universal noise field is postulated in collapse models, inducing appropriate Brownian- motion corrections to standard quantum dynamics. The strength of collapse-driven Brownian fluctuations depend on: (i) the parameters characterizing the system (e.g., mass, size, density), and (ii) two phenomenological parameters defining the statistical properties of the collapse noise. The collapse-driven Brownian motion works such that microscopic systems behave quantum mechanically, while macroscopic objects are classical. At the intermediate mesocopic scale, collapse models predict deviations from standard quantum predictions. This issue has been subject of experimental tests. All experiments to date have been at the scales where collapse effects are negligible for all practical purposes. However, recent experimental progress in revealing quantum features of larger objects, increases the hope for testing at unprecedented scales where collapse models can be falsified. Current experiments are mainly focused on the preparation of macroscopic systems in a spatial quantum superposition state. The collapse effects would then manifest as loss of visibility in the observed inference pattern. However, one needs a quantum interference with single particles of mass ∼ 10 10 amu for a decisive test of collapse models. Creating such massive superpositionsis quite challenging, and beyond currectstate-of-the-art. Quite recently, an alternative approach has been proposed where the collapse manifests in the fluctuating properties of light interacting with the quantum system. The great advantage of this new approach is that here there is no need for the preparation of a quantum superposed state. It has been discussed that promising results can be revealed in the spectrum of light interacting with a radiation pressure-driven mechanical oscillator in a cavity optomechanics setting. Here, we review the theoretical modelling of the above optomechenical proposal. We discuss how collapse-driven Brownian motion modifies the spectrum. We quantify the collapse effect and explain how it depends on the parameters of the mechanical oscillator (e.g., mass, density, geometry).
This chapter introduces cavity quantum optomechanics with levitated nanospheres with some emphasis on preparing mesoscopic quantum superpositions and testing collapse models. It is divided into three parts: levitated quantum optomechanics: atoms vs. sphere; decoherence in levitated nanospheres; and wave-packet dynamics: coherence vs. decoherence. It is first shown how the master equation describing the dynamics of a polarizable object in a cavity along the cavity axis and that of the cavity mode is derived. Optical levitation is also discussed. It is then shown how most of the decoherence sources in levitated nanospheres can be cast into a relatively simple master equation describing position localization type of decoherence. Such decoherence tends to suppress the centre-of-mass position coherences. Finally, a discussion of wave-packet dynamics is given, with the motivation of using levitated nanospheres for matter-wave interferometry, that is, to create macroscopic quantum superpositions for testing quantum mechanics in unprecedented parameter regimes.
Quantum mechanics exhibits a broad collection of theoretical results in complete agreement with experimental evidence. Besides showing unquestionable success in the description of isolated systems, it can be also successfully used to characterize non-isolated quantum system. In such a case, phenomena like dissipation, diffusion or decoherence. The theory of open quantum systems provides the framework where such features can be conveniently explained. \nThis thesis is about decoherence and collapse models. Albeit conceptually they are very far from each other, they both belong the framework of open quantum systems. Indeed, they consider systems interacting with an external entity: an environment for decoherence models, a noise for collapse models. Although the external influence has different origin, they can be described by similar dynamical equations and, to confirm or falsify them, the same experimental tests can be performed. \nThe quantum Brownian motion model can be considered the paradigm of decoherence models. We provide an exact and analytic equation for the time evolution of the operators and we show that the corresponding equation for the states is equivalent to well-known results in the literature. Our derivation allows to compute the time evolution of physically relevant quantities in a much easier way than previous formulations. Moreover, we are not bound to compute the time evolution of the state of the system, which in general is a complicated task. The explicit dependence on the initial state appears only in the initial expectation values and not in the dynamics. This makes possible the derivation of expectation values also for nontrivial states. \nAnother decoherence model we considered is a recently proposed model, based on the mass-energy equivalence. The model describes a decoherence source acting universally on every system whose superposition is extended on positions experiencing different gravitational potentials. We studied the conditions under which this mechanism becomes the dominant decoherence effect in typical interferometric experiments. We show that current experiments are off by several orders of magnitude. New ideas are needed to achieve the necessary requirements. \nThe second part of this thesis concerns collapse models, in particular the Continuous Spontaneous Localization (CSL) model. We focus on experimental tests that can probe it. In this respect, experiments can be grouped in two classes: interferometric tests and non-interferometric ones. The first class includes those experiments, which directly create and detect quantum superpositions of the center of mass of massive systems. The strongest bounds on the CSL parameters come from the second class of non-interferometric experiments, which are sensitive to small position displacements and detect CSL-induced diffusion in position. \nWe investigate how we can benefit from the non-interferometric perspective given by optomechanical setups, which have reached high sensitivities as force and position sensors. Three examples are considered.\nFirst, we compute the upper bounds on the CSL parameters, which can be inferred by the gravitational wave detectors LIGO, LISA Pathfinder and AURIGA.\nSecond, we report new results from an experiment based on a high-quality cantilever cooled to millikelvin temperature. High accuracy measurements of the cantilever thermal fluctuations reveal a nonthermal force noise of unknown origin. This excess noise is compatible with the CSL heating predicted by Adler. Several physical mechanisms able to explain the observed noise have been ruled out.\nThird, we propose an unattempted non-interferometric test aimed to investigate the still unexplored region of the CSL parameter space. Our proposal relies on torsional degrees of freedom rather than the usual vibrational ones. We believe that the test that has been put forward here, will eventually probe the unexplored CSL parameter space.