Abstract We present a simple derivation of the interference pattern in matter-wave interferometry predicted by a class of quantum master equations. We apply the obtained formulae to the following collapse models: the Ghirardi–Rimini–Weber (GRW) model, the continuous spontaneous localization (CSL) model together with its dissipative (dCSL) and non-Markovian generalizations (cCSL), the quantum mechanics with universal position localization (QMUPL), and the Diósi–Penrose (DP) model. We discuss the separability of the dynamics of the collapse models along the three spatial directions, the validity of the paraxial approximation, and the amplification mechanism. We obtain analytical expressions both in the far field and near field limits. These results agree with those already derived in the Wigner function formalism. We compare the theoretical predictions with the experimental data from two recent matter-wave experiments: the 2012 far-field experiment of Juffmann T et al (2012 Nat. Nanotechnol . 7 297–300) and the 2013 Kapitza–Dirac–Talbot–Lau (KDTL) near-field experiment of Eibenberger et al (2013 Phys. Chem. Chem. Phys . 15 14696–700). We show the region of the parameter space for each collapse model that is excluded by these experiments. We show that matter-wave experiments provide model-insensitive bounds that are valid for a wide family of dissipative and non-Markovian generalizations.
Abstract We present a simple derivation of the interference pattern in matter-wave interferometry predicted by a class of quantum master equations. We apply the obtained formulae to the following collapse models: the Ghirardi–Rimini–Weber (GRW) model, the continuous spontaneous localization (CSL) model together with its dissipative (dCSL) and non-Markovian generalizations (cCSL), the quantum mechanics with universal position localization (QMUPL), and the Diósi–Penrose (DP) model. We discuss the separability of the dynamics of the collapse models along the three spatial directions, the validity of the paraxial approximation, and the amplification mechanism. We obtain analytical expressions both in the far field and near field limits. These results agree with those already derived in the Wigner function formalism. We compare the theoretical predictions with the experimental data from two recent matter-wave experiments: the 2012 far-field experiment of Juffmann T et al (2012 Nat. Nanotechnol . 7 297–300) and the 2013 Kapitza–Dirac–Talbot–Lau (KDTL) near-field experiment of Eibenberger et al (2013 Phys. Chem. Chem. Phys . 15 14696–700). We show the region of the parameter space for each collapse model that is excluded by these experiments. We show that matter-wave experiments provide model-insensitive bounds that are valid for a wide family of dissipative and non-Markovian generalizations.
Abstract Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models—Ghirardi–Rimini–Weber (GRW) theory, continuous spontaneous localization (CSL) model, Diósi-Penrose model, and dissipative GRW model—in the Wigner framework. The resulting master equations are approximated by Fokker–Planck equations. Moreover, we use the phase-space form of GRW theory to test, via molecular dynamics simulations, David Albert’s suggestion that the stochasticity induced by spontaneous collapses is responsible for the emergence of thermodynamic irreversibility. The simulations show that, for initial conditions leading to anti-thermodynamic behavior in the classical case, GRW-type perturbations do not lead to thermodynamic behavior. Consequently, the GRW-based equilibration mechanism proposed by Albert is not observed.
We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration space which drives the collapse in a completely deterministic way. This new variable is equivalent to a set of positions of all the particles, i.e., a set of Bohmian positions, which obey the usual guiding equation of Bohmian theory. Any superposition of quantum states of a macroscopic object occupying different regions of space is projected by a localization process onto the region occupied by the positions. Since the Bohmian positions are well defined in a single realization of the experiment, a space localization into one region is produced. The mechanism is based on the correlations between these positions arising from the cohesive forces inside macroscopic objects. The model introduces two collapse parameters which play a role very similar to those of the Ghirardi-Rimini-Weber (GRW) [Ghirardi et al., Phys. Rev. D 34, 470 (1986)] and continuous spontaneous localization (CSL) [Pearle, Phys. Rev. A 39, 2277 (1989); Ghirardi et al., Phys. Rev. A 42, 78 (1990)] theories. With appropriate values of these parameters, we check that the corresponding dynamics rapidly projects superpositions of macroscopic states localized in different regions of space into a single region, while it maintains a negligible effect in all situations where the predictions of standard quantum dynamics are known to be correct. We briefly speculate about the possible relations with gravity. We then study the evolution of the density operator and a mean-field approximation of the dynamical equations of this model, as well as the change of the evolution of the momentum introduced by the localization process. Possible theoretical interpretations are discussed. Generally speaking, this model introduces a sharper border between the quantum and classical worlds than the GRW and CSL theories and leaves a broader range of acceptable values for the parameters.
We have analyzed recently published XENONnT data for the spontaneous X-ray emission signature predicted by the objective wave function collapse model of quantum mechanics. With extremely low background and large exposure, XENONnT data can be used to completely exclude the theoretically predicted collapse parameters of continuous spontaneous localization~(CSL) model suggested by Ghirardi, Rhimini and Weber. Our result strongly suggests that the simplest version of the CSL model with the white-noise assumption is unlikely to provide answers to the long-standing measurement problem of quantum mechanics and motivates pursuits of more complex versions of the theory. If the result is interpreted with the Diósi-Penrose gravitational wave function collapse model, our limit improves the previous limit by a factor of 5.7. Detailed analysis using more precise background modelling can further improve the limits.
Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and flavor-oscillating neutral mesons for the two most promising collapse models, the QMUPL (quantum mechanics with universal position localization) model and the mass-proportional CSL (continuous spontaneous localization) model. Our results are showing (i) a strong sensitivity to the very assumptions of the noise field underlying those two collapse models and (ii) under particular assumptions the CSL case allows one even to recover the decay dynamics. This in turn allows one to predict the effective collapse rates solely based on the measured values for the oscillation (mass differences) and the measured values of the decay constants. The four types of neutral mesons (K meson, D meson, Bd meson, and Bs meson) lead surprisingly to ranges comparable to those put forward by Adler [J. Phys. A: Math. Theor. 40, 2935 (2007)] and Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)]. Our results show that these systems at high energies are very sensitive to possible modifications of the standard quantum theory, making them a very powerful laboratory to rule out certain collapse scenarios and study the detailed physical processes solving the measurement problem.
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.
Quantum mechanics, which governs all microscopic phenomena, encounters challenges when applied to macroscopic objects that exhibit classical behavior. To address this micro-macro disparity, collapse models such as the Continuous Spontaneous Localization (CSL) and Diosi-Penrose (DP) models have been proposed. These models phenomenologically modify quantum theory to reconcile its predictions with the observed classical behavior of macroscopic systems. Based on previous works\,([Phys.\,Rev\,D,\,95(8):084054\,(2017)] and [Phys.\,Rev.\,D,\,94:124036,\,(2016)]), an improved bound on the collapse model parameters is given using the updated acceleration noise data released from LISA Pathfinder\,([Phys.\,Rev.\,D, 110(4):042004,\,(2024)]). The CSL collapse rate is bounded to be at most λCSL≤8.3×10−11\,s−1 at the mili-Hertz band when rCSL=10−7m, and the DP model's regularization cut-off scale is constraint to be σDP∼285.5\,fm. Furthermore, we discuss the potential advantages of using deep-underground laboratories to test these quantum collapse models. Our results show the quiet seismic condition of the current deep-underground laboratory has the potential to further constrain the CSL collapse model to λCSL≤3×10−11s−1 when rCSL=10−7m.