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Collapse models provide a theoretical framework for understanding how classical world emerges from quantum mechanics. Their dynamics preserves (practically) quantum linearity for microscopic systems, while it becomes strongly nonlinear when moving towards macroscopic scale. The conventional approach to test collapse models is to create spatial superpositions of mesoscopic systems and then examine the loss of interference, while environmental noises are engineered carefully. Here we investigate a different approach: We study systems that naturally oscillate --creating quantum superpositions-- and thus represent a natural case-study for testing quantum linearity: neutrinos, neutral mesons, and chiral molecules. We will show how spontaneous collapses affect their oscillatory behavior, and will compare them with environmental decoherence effects. We will show that, contrary to what previously predicted, collapse models cannot be tested with neutrinos. The effect is stronger for neutral mesons, but still beyond experimental reach. Instead, chiral molecules can offer promising candidates for testing collapse models., accepted by NATURE Scientific Reports, 12 pages, 1 figures, 2 tables

Roger Penrose proposed that a spatial quantum superposition collapses as a back-reaction from spacetime, which is curved in different ways by each branch of the superposition. In this sense, one speaks of gravity-related wave function collapse. He also provided a heuristic formula to compute the decay time of the superposition $\mathord{-}$ similar to that suggested earlier by Lajos Di\'osi, hence the name Di\'osi-Penrose model. The collapse depends on the effective size of the mass density of particles in the superposition, and is random: this randomness shows up as a diffusion of the particles' motion, resulting, if charged, in the emission of radiation. Here, we compute the radiation emission rate, which is faint but detectable. We then report the results of a dedicated experiment at the Gran Sasso underground laboratory to measure this radiation emission rate. Our result sets a lower bound on the effective size of the mass density of nuclei, which is about three orders of magnitude larger than previous bounds. This rules out the natural parameter-free version of the Di\'osi-Penrose model., Comment: 66 pages, 7 figures

In this paper we report on the results of two analyses of the data taken with a dedicated VIP-Lead experiment at the Gran Sasso National Laboratory of the INFN. We use measurements taken in an environment that is especially well screened from cosmic rays, with a metal target made of “Roman lead” which is characterised by a low level of intrinsic radioactivity. The analyses lead to an improvement, on the upper bounds of the Pauli Exclusion Principle violation for electrons, which is more than one (four) orders of magnitude, when the electron-atom interactions are described in terms of scatterings (or close encounters) respectively.

The standard scheme of several tests of the Pauli Exclusion Principle in bulk matter — both in the experiment and in the subsequent data analysis — has long been based on the seminal paper by E. Ramberg, G.A. Snow [Phys. Lett. B 238, 438 (1990)]. The ideas exposed in that paper are so simple and immediate that they have long gone unchallenged. However, while some of the underlying approximations are still valid, other parts of the article must be reconsidered. Here, we discuss some new concepts thatare related to the motion of the electrons in the test metal (the “target” of the experiment) and which have been recently studied in the framework of the VIP-2 Collaboration.

The VIP experiment performed an accurate investigation of the Pauli Exclusion Principle for electrons. The apparatus was installed in the Gran Sasso Laboratories of the National Institute of Nuclear Physic in Italy, an underground environment with an extremely low cosmic background. The aim of the experiment was to test the Pauli Exclusion Principle for electrons in a copper target circulated by a Direct Current (DC) current, searching for X-rays emission due to an atomic transition forbidden by Pauli exclusion principle, from the L shell to the K shell of copper when the K shell is already occupied by two electrons. VIP set an upper limit on the Pauli exclusion principle violation probability 1/2β 2 –29. The goal of the upgraded VIP-2 experiment, presently in data taking at Gran Sasso Laboratories, is to improve this limit by two orders of magnitude. The VIP-2 experimental apparatus, in which the Silicon Drift Detectors have the key role of X-ray detectors, and preliminary results are presented.

The VIP Collaboration is performing high precision tests of the Pauli Exclusion Principle for electrons in the extremely low cosmic background environment of the Underground Gran Sasso Laboratories of INFN (Italy). The experimental technique consists in introducing a DC current in a copper conductor, searching for Kα PEP-forbidden atomic transitions when the K shell is already occupied by two electrons. VIP set an upper limit on the PEP-violation probability (½) x β^2 < 4.7 × 10^−29. The aim of the upgraded VIP-2 experiment is to improve this result at least by two orders of magnitude. The improved experimental setup and the results of a preliminary data analysis, corresponding to the the first run of the VIP-2 data taking (2016–2017), will be presented.

The VIP-2 (VIolation of the Pauli Exclusion Principle) experiment conducted at the Gran Sasso underground laboratory (LNGS) of INFN is searching for possible tiny violations of standard quantum mechanics in copper atoms with extremely high sensitivity. We investigate atomic transitions with precision X-ray spectroscopy in order to test the Pauli Exclusion Principle (PEP) and therefore the spin-statistics theorem. We present the experimental method for the search for "anomalous" (i.e. Pauli-forbidden) X-ray transitions in copper atoms, produced by "new" electrons, which could have a tiny probability to undergo a Pauli-forbidden transition to the 1s ground state already occupied by two electrons. We describe the VIP-2 experimental setup and its recent optimisations. Presently VIP-2 is taking data at LNGS. The goal of VIP-2 is to test PEP for electrons with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10-31 (and using a more elaborate analysis even 10-40). We present current experimental results.

The VIP2 (VIolation of the Pauli Exclusion Principle) experiment at the Gran Sasso underground laboratory (LNGS) is searching for possible violations of standard quantum mechanics predictions in atoms at very high sensitivity. We investigate atomic transitions with precision X-ray spectroscopy in order to test the Pauli Exclusion Principle (PEP) and therefore the related spin-statistics theorem. We will present our experimental method for the search for "anomalous" (i.e. Pauli-forbidden) X-ray transitions in copper atoms, produced by "new" electrons, which could have tiny probability to undergo Pauli-forbidden transition to the ground state already occupied by two electrons. We will describe the VIP2 experimental setup, which is taking data at LNGS presently. 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 will present current experimental results and discuss implications of a possible violation., Comment: Proceedings of DICE 2018 Conference

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.

In the VIP2 (VIolation of the Pauli Exlusion Principle) experiment at the Gran Sasso underground laboratory (LNGS) we are searching for possible violations of standard quantum mechanics predictions. With high precision we investigate the Pauli Exclusion Principle and the collapse of the wave function (collapse models). We will present our experimental method of searching for possible small violations of the Pauli Exclusion Principle for electrons, via the search for "anomalous" X-ray transitions in copper atoms, produced by "new" electrons (brought inside a copper bar by circulating current) which could have the probability to undergo Pauli-forbidden transition to the ground state (1 s level) already occupied by two electrons. We will describe the concept of the VIP2 experiment taking data at LNGS presently. 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 will show preliminary experimental results obtained at LNGS and discuss implications of a possible violation., Comment: Proceedings TAUP 2017

International audience; 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 compute the effect of collapse models on neutrino oscillations. The effect of the collapse is to modify the evolution of the `spatial' part of the wave function, which indirectly amounts to a change on the flavor components. In many respects, this phenomenon is similar to neutrino propagation through matter. For the analysis we use the mass proportional CSL model, and perform the calculation to second order perturbation theory. As we will show, the CSL prediction is very small - mainly due to the very small mass of neutrinos - and practically undetectable., Comment: 24 pages, RevTeX. Updated version

The Pauli exclusion principle (PEP), consequence of the spin-statistics connection, is one of the basic principles of the modern physics. Being at the very basis of our understanding of matter, as many other fundamental principles it spurs a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the violation parameter q translates into a probability of violating PEP. The VIP (VIolation of the Pauli exclusion principle) experiment established a new limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter from quon theory and as probability of PEP violation, we briefly discuss them and present future plans to go beyond the actual limit by upgrading the experimental setup. We also shortly mention the possibility of using a similar experimental technique to search for eventual X-rays, generated in the spontaneous collapse models in quantum mechanics.

Many experiments investigated the violation of the Pauli Exclusion Principle (PEP) since its discovery in 1925. The VIP (VIolation of the Pauli Principle) experiment tested the PEP by measuring the probability for an external electron to be captured and undergo a 2p to 1s transition during its cascading process, where the 1s state is already occupied by two electrons. This transition is forbidden by the Pauli Exclusion Principle. The VIP experiment resulted in a preliminary upper limit for the probability of the violation of the PEP of 4.7 x 10^{-29}. Currently a setup for the follow-up experiment VIP 2 is under preparation. The goal of this experiment is to improve the upper limit for the violation of the PEP by two orders of magnitude, by different improvements like enhanced energy resolution of the X-ray detectors and by implementing an active shielding. Here we report currently ongoing performance tests of the new parts of the setup., EXA 2014 proceedings in Hyperfine Interactions (2015), Springer International Publishing

The Pauli Exclusion Principle is one of the most fundamental rules of nature and represents a pillar of modern physics. According to many observations the Pauli Exclusion Principle must be extremely well fulfilled. Nevertheless, numerous experimental investigations were performed to search for a small violation of this principle. The VIP experiment at the Gran Sasso underground laboratory searched for Pauli-forbidden X-ray transitions in copper atoms using the Ramberg-Snow method and obtained the best limit so far. The follow-up experiment VIP2 is designed to reach even higher sensitivity. It aims to improve the limit by VIP by orders of magnitude. The experimental method, comparison of different PEP tests based on different assumptions and the developments for VIP2 are presented., Comment: 6 pages, 3 figures, Proceedings DISCRETE2014 Conference

High-precision experiments have been done to test the Pauli exclusion principle (PEP) for electrons by searching for anomalous $K$-series X-rays from a Cu target supplied with electric current. With the highest sensitivity, the VIP (VIolation of Pauli Exclusion Principle) experiment set an upper limit at the level of $10^{-29}$ for the probability that an external electron captured by a Cu atom can make the transition from the 2$p$ state to a 1$s$ state already occupied by two electrons. In a follow-up experiment at Gran Sasso, we aim to increase the sensitivity by two orders of magnitude. We show proofs that the proposed improvement factor is realistic based on the results from recent performance tests of the detectors we did at Laboratori Nazionali di Frascati (LNF)., Comment: 8 pages, 5 figures, conference proceedings on TAUP 2013

In the last decades huge theoretical effort was devoted to the development of consistent theoretical models, aiming to solve the so-called "measurement problem". Among these, the Dynamical Reduction Models possess the unique characteristic to be experimentally testable, thus enabling to set experimental upper bounds on the reduction rate parameter λ characterizing these models. By analysing the X-ray spectrum emitted by an isolated slab of Germanium, we set the most stringent limit on the λ parameter up to date.

1 ar X iv :1 50 1. 04 46 2v 1 [ qu an tph ] 1 9 Ja n 20 15 The development of mathematically complete and consistent models solving the so-called ”measurement problem”, strongly renewed the interest of the scientific community for the foundations of quantum mechanics, among these the Dynamical Reduction Models posses the unique characteristic to be experimentally testable. In the first part of the paper an upper limit on the reduction rate parameter of such models will be obtained, based on the analysis of the X-ray spectrum emitted by an isolated slab of germanium and measured by the IGEX experiment. The second part of the paper is devoted to present the results of the VIP (Violation of the Pauli exclusion principle) experiment and to describe its recent upgrade. The VIP experiment established a limit on the probability that the Pauli Exclusion Principle (PEP) is violated by electrons, using the very clean method of searching for PEP forbidden atomic transitions in copper. 1 Upper limit on the wave function collapse mean rate parameter λ The first consistent and satisfying Dynamical Reduction Model, known as Quantum Mechanics with Spontaneous Localization (QMSL) [1], considers particles undergoing spontaneous localizations around definite positions, following a Possion distribution characterized by a mean frequency λ = 10−16 s−1. This brought to the development of the CSL theory [2] based on the introduction of new, non linear and stochastic terms, in the Shrodinger equation besides to the standard Hamiltonian. Such terms induce, for the state vector, a diffusion process, which is responsible for the wave packet reduction. As demonstrated by Q. Fu [3] the particle interaction with the stochastic field also causes an enhancement of the energy expectation value. This implies, for a charged particle, the emission of electromagnetic radiation (known as spontaneous radiation) not present in the standard quantum mechanics. The radiation spectrum spontaneously emitted by a free electron was calculated by Fu [3] in the framework of the non-relativistic CSL model, and it is given by: dΓ(E) dE = eλ 4π2a2m2E , where m represents the electron mass, E is the energy of the emitted photon, λ and a are respectively the reduction rate parameter and the correlation length of the reduction model which is assumed to be a = 10−7 m. If the stochastic field is assumed to be coupled to the particle mass density (mass proportional CSL model) (see for example [4]) then the previous expression for the emission rate is to be multiplied by the factor (me/mN ) , with mN the nucleon mass. Using the measured radiation appearing in an isolated slab of Germanium [5] corresponding to an energy of 11 KeV, Fu obtained the limit λ ≤ 0.55 · 10−16s−1. In Ref. [6] the author argues that, in evaluating his numerical result, Fu uses for the electron charge the value e = 17137.04, whereas the standard adopted Feynman rules require the identification e/(4π) = 17137.04. We took into account this correction when evaluating the new limit. In order to reduce possible biases introduced on the λ value by the punctual evaluation of the rate at one single energy bin, the X-ray emission spectrum measured by the IGEX experiment [7, 8] was fitted in the range ∆E = 4.5÷ 48.5 KeV m, compatible with the non-relativistic assumption (for electrons) used in the calculation of the predicted rate. A Bayesian model was

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"., 7 pages, 3 figures, proceedings to the workshop "Eighth International Workshop DICE2016", Castello Pasquini/Castiglioncello (Tuscany), September 12-16, 2016 Spacetime - Matter - Quantum Mechanics

The Pauli exclusion principle (PEP) is one of the basic principles of the modern physics. Being at the very basis of our understanding of matter, it spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the violation parameter q translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the violation parameter to a value very close to either 1 (for bosons) or -1 (for fermions). The VIP (VIolation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter from quon theory and as probability of PEP violation, we briefly discuss them and present future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopical fast Silicon Drift Detectors. We also mention the possibility of using a similar experimental technique to search for eventual X-rays, generated in the spontaneous collapse models.

The Pauli exclusion principle (PEP) and, more generally, the spin-statistics connection, is at the very basis of our understanding of matter and Nature. The PEP spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Mechanics and Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible small violation of PEP, where the q violation parameter translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the q-parameter to a value very close to either 1 (for bosons) or −1 (for fermions). The VIP (VIolation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the very clean method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter and as probability of PEP violation, we briefly discuss the results and present plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopic fast Silicon Drift Detectors. We discuss as well the possibility of using a similar experimental technique to search for X-rays generated as a signature of the spontaneous collapse of the wave function, predicted by continuous spontaneous localization type theories.

One of the fundamental rules of nature and a pillar in the foundation of quantum theory and thus of modern physics is represented by the Pauli Exclusion Principle. We know that this principle is extremely well fulfilled due to many observations like the order of the elements and the stability of matter. Numerous experiments were performed to search for tiny violation of this rule in various systems. The VIP experiment at Gran Sasso underground laboratory is testing the validity of this principle for electrons with very high precision (order of 10−30). The layout of the present experiment, results obtained so far and new ideas to further increase the precision will be presented.

The VIP (Violation of the Pauli Exclusion Principle) experiment is investigating one of the basic principles of modern physics, searching for anomalous X-rays emitted by copper atoms in a conductor: any detection of these anomalous X-rays would mark a Pauli forbidden transition. VIP is currently taking data at the Gran Sasso underground laboratories, and its scientific goal is to improve by three-four orders of magnitude the previous limit on the probability of Pauli violating transitions, bringing it into the 10-29÷-30 region. The new experimental results, together with future plans, are presented.

Many experiments investigated the possible violation of the Pauli Exclusion Principle (PEP) since its discovery in 1925. The VIP(Violation of the Pauli Principle) experiment tested the PEP by measuring the probability for an external electron to be captured and undergo a 2p to 1s transition during its cascading process, with the 1s state already occupied by two electrons. This transition is forbidden by the PEP. The VIP experiment resulted in an upper limit for the probability of PEP violation of 4.7 × 10−29. Currently a setup for the follow up experiment VIP2 is under preparation. The goal of this experiment is to improve the upper limit for the violation of the PEP by two orders of magnitude, by using new X-ray detectors and by implementing an active shielding. We then present the idea of using an analogous experimental technique to search for X rays as a signature of the spontaneous collapse of the wave function, predicted by the continuous spontaneous localization theories, and discuss some very encouraging preliminary results.

The Pauli exclusion principle (PEP) and, more generally, the spin-statistics connection, is at the very basis of our understanding of matter. The PEP spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the q violation parameter translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the q-parameter to a value very close to either 1 (for bosons) or -1 (for fermions). The VIP (Violation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter and as probability of PEP violation, we briefly discuss the results and present future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopic fast Silicon Drift Detectors. We mention as well the possibility of using a similar experimental technique to search for eventual X-rays generated as a signature of the spontaneous collapse of the wave function, predicted by continuous spontaneous localization type theories.

One of the fundamental rules of nature and a pillar in the foundation of quantum theory and thus of modern physics is represented by the Pauli Exclusion Principle. We know that this principle is extremely well fulfilled due to many observations. Numerous experiments were performed to search for tiny violation of this rule in various systems. The experiment VIP at the Gran Sasso underground laboratory is searching for possible small violations of the Pauli Exclusion Principle for electrons leading to forbidden X-ray transitions in copper atoms. VIP is aiming at a test of the Pauli Exclusion Principle for electrons with high accuracy, down to the level of 10$^{-29}$ - 10$^{-30}$, thus improving the previous limit by 3-4 orders of magnitude. The experimental method, results obtained so far and new developments within VIP2 (follow-up experiment at Gran Sasso, in preparation) to further increase the precision by 2 orders of magnitude will be presented., Proceedings DISCRETE 2012-Third Symposium on Prospects in the Physics of Discrete Symmetries, Lisbon, December 3-7, 2012