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What gravitational field is generated by a massive quantum system in a spatial superposition? Despite decades of intensive theoretical and experimental research, we still do not know the answer. On the experimental side, the difficulty lies in the fact that gravity is weak and requires large masses to be detectable. However, it becomes increasingly difficult to generate spatial quantum superpositions for increasingly large masses, in light of the stronger environmental effects on such systems. Clearly, a delicate balance between the need for strong gravitational effects and weak decoherence should be found. We show that such a trade off could be achieved in an optomechanics scenario that allows to witness whether the gravitational field generated by a quantum system in a spatial superposition is in a coherent superposition or not. We estimate the magnitude of the effect and show that it offers perspectives for observability.

Collapse models describe phenomenologically the quantum-to-classical transition by adding suitable nonlinear and stochastic terms to the Schrödinger equation, thus (slightly) modifying the dynamics of quantum systems. Experimental bounds on the collapse parameters have been derived from various experiments involving a plethora of different systems, from single atoms to gravitational wave detectors. Here, we give a comprehensive treatment of the continuous spontaneous localization (CSL) model, the most studied among collapse models, for Fermi liquids. We consider both the white and non-white noise case. Application to various astrophysical sources is presented.

In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another one defined on a Hilbert space with stochastic integration measure (stochastic time-dependent scalar product). The formulations of the two problems and a comparison with the general theory of open quantum systems are discussed. Possible physical applications of the situations considered are analyzed.

Wave function collapse models assume that the Schrödinger equation is not entirely right, and must be supplemented with extra terms, which cause the (random) collapse of the wave function. In some of these models, the collapse is linked to gravity. We review the most popular gravitational wave function collapse models, with an emphasis on their conceptual status, stage of development, comparison with experiments, and open questions.

Collapse models implement a progressive loss of quantum coherence when the mass and the complexity of quantum systems increase. We will review such models and the current attempts to test their predicted loss of quantum coherence.

Gravitational decoherence and gravitational wave function collapse are presented as two related but conceptually distinct ideas. Gravitational decoherence measures the effect of gravitational perturbations on the evolution of quantum systems, in particular their progressive lack of coherence. Gravitational wave function collapse starts with the assumption that the Schrodinger equation is not entirely right, and must be supplemented with extra terms, which cause the (random) collapse of the wave function; the collapse is then linked to gravity. Some of the most popular models are reviewed, with an emphasis on their conceptual status, stage of development, and open questions.

The continuous spontaneous localization (CSL) model strives to describe the quantum-to-classical transition from the viewpoint of collapse models. However, its original formulation suffers from a fundamental inconsistency in that it is explicitly energy nonconserving. Fortunately, a dissipative extension to CSL has been recently formulated that solves such an energy-divergence problem. We compare the predictions of the dissipative and nondissipative CSL models when various optomechanical settings are used and contrast such predictions with available experimental data, thus building the corresponding exclusion plots.

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: [Figure not available: see fulltext.].

Recently, nonthermal excess noise, compatible with the theoretical prediction provided by collapse models, was measured in a millikelvin nanomechanical cantilever experiment [A. Vinante, Phys. Rev. Lett. 119, 110401 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.110401]. We propose a feasible implementation of the cantilever experiment able to probe such noise. The proposed modification, completely within the grasp of current technology and readily implementable also in other types of mechanical noninterferometric experiments, consists in replacing the homogeneous test mass with one composed of different layers of different materials. This will enhance the action of a possible collapse noise above that given by standard noise sources.

The continuous spontaneous localization (CSL) model is the best known and studied among collapse models, which modify quantum mechanics and identify the fundamental reasons behind the unobservability of quantum superpositions at the macroscopic scale. Albeit several tests were performed during the last decade, up to date the CSL parameter space still exhibits a vast unexplored region. Here, we study and propose an unattempted non-interferometric test aimed to fill this gap. We show that the angular momentum diffusion predicted by CSL heavily constrains the parametric values of the model when applied to a macroscopic object.

In this report, we present a quantum theory describing the propagation of the electromagnetic radiation in a fiber in the presence of the third order dispersion coefficient. We obtained the quantum photon-polariton field, hence, we provide herein a coupled set of operator forms for the corresponding nonlinear Schrödinger equations when the third order dispersion coefficient is included. Coupled stochastic nonlinear Schrödinger equations were obtained by applying a positive P-representation that governs the propagation and interaction of quantum solitons in the presence of the third-order dispersion term. Finally, to reduce the fluctuations near solitons in the first approximation, we developed coupled stochastic linear equations.

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.

We are experimentally investigating possible violations of standard quantum mechanics predictions in the Gran Sasso underground laboratory in Italy. We test with high precision the Pauli exclusion principle and the collapse of the wave function (collapse models). We present our method of searching for possible small violations of the Pauli exclusion principle (PEP) for electrons, through the search for anomalous X-ray transitions in copper atoms, produced by fresh electrons (brought inside the copper bar by circulating current) which could have a non-zero probability to undergo Pauli-forbidden transition to the 1s level already occupied by two electrons, and we describe the VIP2 (Violation of PEP) experiment under data taking at the Gran Sasso underground laboratories. In this paper the new VIP2 setup installed in the Gran Sasso underground laboratory will be presented. The goal of VIP2 is to test the PEP for electrons with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10−31. We show preliminary experimental results and discuss implications of a possible violation.

Matter-wave interferometry is a direct test of the quantum superposition principle for massive systems, and of collapse models. Here we show that the bounds placed by matter-wave interferometry depend weakly on the details of the collapse mechanism. Specifically, we compute the bounds on the CSL model and its variants, provided by the KDTL interferometry experiment of Arndt's group (Eibenberger et al. (2013) [3]), which currently holds the record of largest mass in interferometry. We also show that the CSL family of models emerges naturally by considering a minimal set of assumptions. In particular, we construct the dynamical map for the colored and dissipative Continuous Spontaneous Localization (cdCSL) model, which reduces to the CSL model and variants in the appropriate limits. In addition, we discuss the measure of macroscopicity based on the cdCSL model.

By performing X-ray measurements in the "cosmic silence"of the underground laboratory of Gran Sasso, LNGS-INFN, we test a basic principle of quantum mechanics: The Pauli Exclusion Principle (PEP) for electrons. We present the achieved results of the VIP experiment and the ongoing VIP2 measurement aiming to gain two orders of magnitude improvement in testing PEP. X-ray emission can also be used to put strong constraints on the parameters of the Continuous Spontaneous Localization Model, which was introduced as a possible solution to the measurement problem in Quantum Mechanics. A Bayesian analysis of the data collected by IGEX will be presented, which allows to exclude a broad region of the parameter space which characterizes this model.

We discuss effects of loss of coherence in low energy quantum systems caused by or related to gravitation, referred to as gravitational decoherence. These effects, resulting from random metric fluctuations, for instance, promise to be accessible by relatively inexpensive table-top experiments, way before the scales where true quantum gravity effects become important. Therefore, they can provide a first experimental view on gravity in the quantum regime. We will survey models of decoherence induced both by classical and quantum gravitational fluctuations; it will be manifest that a clear understanding of gravitational decoherence is still lacking. Next we will review models where quantum theory is modified, under the assumption that gravity causes the collapse of the wave functions, when systems are large enough. These models challenge the quantum-gravity interplay, and can be tested experimentally. In the last part we have a look at the state of the art of experimental research. We will review efforts aiming at more and more accurate measurements of gravity (G and g) and ideas for measuring conventional and unconventional gravity effects on nonrelativistic quantum systems.

Spontaneous collapse models predict that a weak force noise acts on any mechanical system, as a consequence of the collapse of the wave function. Significant upper limits on the collapse rate have been recently inferred from precision mechanical experiments, such as ultracold cantilevers and the space mission LISA Pathfinder. Here, we report new results from an experiment based on a high-Q cantilever cooled to millikelvin temperatures, which is potentially able to improve the current bounds on the continuous spontaneous localization (CSL) model by 1 order of magnitude. 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.

We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we consider translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined by Nimmrichter and Hornberger [Phys. Rev. Lett. 110, 16 (2013)PRLTAO0031-9007].

By performing X-rays measurements in the "cosmic silence" of the underground laboratory of Gran Sasso, LNGS-INFN, we test a basic principle of quantum mechanics: the Pauli Exclusion Principle (PEP), for electrons. We present the achieved results of the VIP experiment and the ongoing VIP2 measurement aiming to gain two orders of magnitude improvement in testing PEP. We also use a similar experimental technique to search for radiation (X and gamma) predicted by continuous spontaneous localization models, which aim to solve the "measurement problem".