New experimental limit on Pauli Exclusion Principle violation by electrons (the VIP experiment)

VIP 2: Experimental tests of the Pauli Exclusion Principle for electrons

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 experi…

The VIP Experiment

The Pauli Exclusion Principle (PEP) is a basic principle of Quantum Mechanics, and its validity has never been seriously challenged. However, given its importance, it is very important to check it as thoroughly as possible. Here we describe the VIP (Violation of PEP) experiment, an improved version of the Ramberg and Snow experiment (Ramberg and Snow, Phys. Lett. B238 (1990) 438); VIP shall be performed at the Gran Sasso underground laboratories, and aims to test the Pauli Exclusion Principle for electrons with unprecedented accuracy, down to $\frac{β^2}{2} \sim 10^{-30}$

VIP-2 at LNGS: An experiment on the validity of the Pauli Exclusion Principle for electrons

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. These transitions are produced by new electrons (brought inside the copper bar by circulating current) which can have the possibility to undergo Paul…

The Pauli exclusion principle and beyond

The Pauli exclusion principle can be stated as inequality $<ψ|ρ|ψ>\le 1$ for the electron density matrix $ρ$. Nowadays it is replaced by skew symmetry of the multi-electron wave function. The replacement leads to numerous additional constraints on $ρ$, which are discussed in this letter together with their physical implications, in particular for spin magnetic moment of a multi-electron system.

Experimental Data from a Quantum Computer Verifies the Generalized Pauli Exclusion Principle

"What are the consequences ... that Fermi particles cannot get into the same state ... " R. P. Feynman wrote of the Pauli exclusion principle, "In fact, almost all the peculiarities of the material world hinge on this wonderful fact." In 1972 Borland and Dennis showed that there exist powerful constraints beyond the Pauli exclusion principle on the orbital occupations of Fermi particles, providing important restrictions on quantum correlation and entanglement. Here we use computations on quantum computers to experimentally verify the existence of these additional constraints. Quantum many-ferm…

VIP2 at Gran Sasso - Test of the validity of the spin statistics theorem for electrons with X-ray spectroscopy

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) w…

Detector setup of the VIP2 Underground Experiment at LNGS

The VIP2 experiment tests the Pauli Exclusion Principle with high sensitivity, by searching for Pauli-forbidden atomic transitions from the 2p to the 1s shell in copper at about 8keV. The transition energy of Pauli-forbidden K X-rays is shifted by about 300 eV with respect to the normal allowed K line. This energy difference can be resolved using Silicon Drift Detectors. The data for this experiment is taken in the Gran Sasso underground laboratory (LNGS), which provides shielding from cosmic radiation. An overview of the detection system of the VIP2 experiment will be given. This includes the…

Underground test of quantum mechanics - the VIP2 experiment

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 can have the probability to undergo Pauli-forbidden transiti…

New experimental limit on the Pauli Exclusion Principle violation by electrons

The Pauli Exclusion Principle (PEP) is one of the basic principles of modern physics and, even if there are no compelling reasons to doubt its validity, it is still debated today because an intuitive, elementary explanation is still missing, and because of its unique stand among the basic symmetries of physics. The present paper reports a new limit on the probability that PEP is violated by electrons, in a search for a shifted K$_α$ line in copper: the presence of this line in the soft X-ray copper fluorescence would signal a transition to a ground state already occupied by 2 electrons. The ob…

q-deformed fermion oscillators, zero-point energy and inclusion-exclusion principle

The theory of Fermion oscillators has two essential ingredients: zero-point energy and Pauli exclusion principle. We devlop the theory of the statistical mechanics of generalized q-deformed Fermion oscillator algebra with inclusion principle (i.e., without the exclusion principle), which corresponds to ordinary fermions with Pauli exclusion principle in the classical limit $q \to 1$. Some of the remarkable properties of this theory play a crucial role in the understanding of the q-deformed Fermions. We show that if we insist on the weak exclusion principle, then the theory has the expected low…

Influence of the Fermionic Exchange Symmetry beyond Pauli's Exclusion Principle

Pauli's exclusion principle has a strong impact on the properties of most fermionic quantum systems. Remarkably, the fermionic exchange symmetry implies further constraints on the one-particle picture. By exploiting those generalized Pauli constraints we derive a measure which quantifies the influence of the exchange symmetry beyond Pauli's exclusion principle. It is based on a geometric hierarchy induced by the exclusion principle constraints. We provide a proof of principle by applying our measure to a simple model. In that way, we conclusively confirm the physical relevance of the generaliz…

Bell's inequality, the Pauli exclusion principle and baryonic structure

Bell's inequality has been traditionally used to explore the relationship between hidden variables and the Copenhagen interpretation of quantum mechanics. In this paper, another use is found. Bell's inequality is used to derive a coupling principle for elementary particles and to give a deeper understanding of baryonic structure. We also give a derivation of the Pauli exclusion principle from the coupling principle. Pacs: 14.20-c, 12.90+b, 3.65.Bz, 12.40.Ee

The Pauli Exclusion Operator: example of Hooke's atom

The Pauli Exclusion Operator (PEO) which ensures proper symmetry of the eigenstates of multi-electron systems with respect to exchange of each pair of electrons is introduced. Once PEO is added to the Hamiltonian, no additional constraints on multi-electron wave function due to the Pauli exclusion principle are needed. For two-electron states in two dimensions ($2D$) the PEO can be expressed in a closed form in terms of momentum operators, while in the position representation PEO is a non-local operator. Generalizations of PEO for multi-electron systems is introduced. Several approximations to…

Beyond quantum mechanics? Hunting the 'impossible' atoms (Pauli Exclusion Principle violation and spontaneous collapse of the wave function at test)

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…

Influence of the Pauli exclusion principle on scattering properties of cobosons

We examine the influence of the Pauli exclusion principle on the scattering properties of composite bosons (cobosons) made of two fermions, such as the exciton quasiparticle. The scattering process incorporates boson-phonon interactions that arise due to lattice vibrations. Composite boson scattering rates increase with the entanglement between the two fermionic constituents, which comes with a larger number of available single-fermion states. An important role is played by probabilities associated with accommodating an incoming boson among the remaining unoccupied Schmidt modes in the initial…

Testing the Pauli Exclusion Principle for electrons at LNGS

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 …

Pilot Wave Steerage: A Mechanism and Test

An intuitive, generic, physical model, or conceptual paradigm for pilot wave steerage of particle beams based on Stochastic Electrodynamics is presented. The utility of this model for understanding the Pauli Exclusion Principle is briefly considered, and a possible experimental verification for the underlying concepts is proposed. \\[7mm] Key words: Quantum Mechanics, Pilot Wave, Pauli Exclusion Principle, Stochastic Electrodynamics

The Pauli principle revisited

By the Pauli exclusion principle no quantum state can be occupied by more than one electron. One can put it as a constraint on the electron density matrix that bounds its eigenvalues by 1. Shortly after its discovery the Pauli principle has been replaced by skew symmetry of a multi-electron wave function. In this paper we solve a longstanding problem about the impact of this replacement on the electron density matrix, that goes far beyond the original Pauli principle.

Rotational invariance and the Pauli exclusion principle

In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This will be referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. Finally, the experimental evidence to…

The Role of Nonequilibrium LO Phonons, Pauli Exclusion, and Intervalley Pathways on the Relaxation of Hot Carriers in InGaAs Multi-Quantum-Well Structures

Under continuous-wave laser excitation in an InGaAs multi-quantum-well (MQW) structure, the carrier temperature extracted from photoluminescence rises faster for 405 nm excitation compared with 980 nm excitation, as the injected carrier density increases. Ensemble Monte Carlo simulation of the carrier dynamics in the MQW system shows that this carrier temperature rise is dominated by nonequilibrium LO phonon effects, with the Pauli exclusion having a significant effect at high carrier densities. Further, we find a significant fraction of carriers reside in the satellite L-valleys for 405 nm ex…

Experimental search for the violation of Pauli Exclusion Principle

The VIolation of Pauli exclusion principle -2 experiment, or VIP-2 experiment, at the Laboratori Nazionali del Gran Sasso searches for x-rays from copper atomic transition that are prohibited by the Pauli Exclusion Principle. Candidate direct violation events come from the transition of a $2p$ electron to the ground state that is already occupied by two electrons. From the first data taking campaign in 2016 of VIP-2 experiment, we determined a best upper limit of 3.4 $\times$ 10$^{-29}$ for the probability that such a violation exists. Significant improvement in the control of the experimental…

在LNGS利用Gator探测器搜寻泡利不相容原理的违反现象

Search for Pauli Exclusion Principle Violations with Gator at LNGS

本研究利用LNGS的低本底高纯锗探测器Gator，通过满足Messiah-Greenberg超选择定则的实验技术检验铅原子中违反泡利不相容原理的跃迁，未观测到违反现象，将相关概率上限约束提升一个数量级以上。

Compositeness effects, Pauli's principle and entanglement

We analyse some compositeness effects and their relation with entanglement. We show that the purity of a composite system increases, in the sense of the expectation values of the deviation operators, with large values of the entanglement between the components of the system. We also study the validity of Pauli's principle in composite systems. It is valid within the limits of application of the approach presented here. We also present an example of two identical fermions, one of them entangled with a distinguishable particle, where the exclusion principle cannot be applied. This result can be …

BCS-BEC 交叉中的等自旋和反自旋密度-密度关联：规范对称性、泡利不相容原理、威克定理与实验

Equal-spin and opposite-spin density-density correlations in the BCS-BEC crossover: Gauge Symmetry, Pauli Exclusion Principle, Wick's Theorem and Experiments

基于规范不变性和泡利原理，建立了自旋相关密度-密度关联的约束，并通过二维零温BCS到玻色区间的计算，揭示了两粒子不可约贡献（集体激发、多粒子散射和顶点修正）对描述实验的关键作用，特别是解释了反自旋密度-密度关联中实验观测到的极小值。

Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle

We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems beyond the ground state. Various obstacles which historically have doomed such an approach to be unfeasible are overcome. First, we resort to a generalization of the Ritz variational principle to ensemble states with fixed weights. This in combination with the constrained search formalism allows us to establish a universal functional of the one-particle reduced density matrix. Second, we employ tools from convex analysis to circumvent the too i…

Dirac's hole theory and the Pauli principle: clearing up the confusion

In Dirac's hole theory (HT) the vacuum state is generally believed to be the state of minimum energy due to the assumption that the Pauli Exclusion Principle prevents the decay of positive energy electrons into occupied negative energy states. However recently papers have appeared that claim to show that there exist states with less energy than that of the vacuum[4][5][6]. Here we will consider a simple model of HT consisting of zero mass electrons in 1-1D space-time. It will be shown that for this model there are states with less energy than the HT vacuum state and that the Pauli Principle is…

Pauli Exclusion Principle and its theoretical foundation

The modern state of the Pauli Exclusion Principle (PEP) is discussed. PEP can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is the so-called spin-statistics connection (SSC). As we will discuss, the physical reasons why SSC exists are still unknown. On the other hand, according to PEP, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, both…

How Electronic Dynamics with Pauli Exclusion Produces Fermi-Dirac Statistics

It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old …

Validity of Feynman's prescription of disregarding the Pauli principle in intermediate states

Regarding the Pauli principle in quantum field theory and in many-body quantum mechanics, Feynman advocated that Pauli's exclusion principle can be completely ignored in intermediate states of perturbation theory. He observed that all virtual processes (of the same order) that violate the Pauli principle cancel out. Feynman accordingly introduced a prescription, which is to disregard the Pauli principle in all intermediate processes. This ingeneous trick is of crucial importance in the Feynman diagram technique. We show, however, an example in which Feynman's prescription fails. This casts dou…

The Role of the Exclusion Principle for Atoms to Stars: A Historical Account

In a first historical part I shall give a detailed description of how Pauli discovered --before the advent of the new quantum mechanics -- his exclusion principle. The second part is devoted to the insight and results that have been obtained in more recent times in our understanding of the stability of matter in bulk, both for ordinary matter (like stones) and self-gravitating bodies.

Useful entanglement from the Pauli principle

We address the question whether identical-particle entanglement is a useful resource for quantum information processing. We answer this question positively by reporting a scheme to create entanglement using semiconductor quantum wells. The Pauli exclusion principle forces quantum correlations between the spins of two independent fermions in the conduction band. Selective electron-hole recombination then transfers this entanglement to the polarization of emitted photons, which can subsequently be used for quantum information tasks.

Observation of Pauli Crystals

The Pauli exclusion principle is a fundamental law underpinning the structure of matter. Due to their anti-symmetric wave function, no two fermions can occupy the same quantum state. Here, we report on the direct observation of the Pauli principle in a continuous system of up to six particles in the ground state of a two-dimensional harmonic oscillator. To this end, we sample the full many-body wavefunction by applying a single atom resolved imaging scheme in momentum space. We find so-called Pauli crystals as a manifestation of higher order correlations. In contrast to true crystalline phases…

Underground tests of quantum mechanics. Whispers in the cosmic silence?

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".

Statistical Mechanical Interpretation of 2D Pauli Crystals

A manifestation of the Pauli Exclusion Principle is observed when fermions are trapped in the ground state of a 2D harmonic oscillator trap at very low temperatures. This non-interaction of fermions results in the formation of Pauli crystals. This work introduces a statistical mechanical interpretation of the principles that led to the observation of Pauli crystals by calculating the energy, radius and other parameters of the non-interacting arrangement of ultra-cold fermions. This model approaches the problem from two different directions, namely fermion degeneracy and harmonic oscillator tre…

On the observability of Pauli crystals

The best known manifestation of the Fermi-Dirac statistics is the Pauli exclusion principle: no two identical fermions can occupy the same one-particle state. This principle enforces high order correlations in systems of many identical fermions and is responsible for a particular geometric arrangement of trapped particles even when all mutual interactions are absent [1]. These geometric structures, called Pauli crystals, are predicted for a system of $N$ identical atoms trapped in a harmonic potential. They emerge as the most frequent configurations in a collection of single-shot pictures of t…

New Perspectives on the Schr{ö}dinger-Pauli Theory of Electrons: Part II: Application to the Triplet State of a Quantum Dot in a Magnetic Field

The Schrödinger-Pauli theory of electrons in the presence of a static electromagnetic field can be described from the perspective of the individual electron via its equation of motion or `Quantal Newtonian' first law. The law is in terms of `classical' fields whose sources are quantum-mechanical expectation values of Hermitian operators taken with respect to the wave function. The law states that the sum of the external and internal fields experienced by each electron vanishes. The external field is the sum of the binding electrostatic and Lorentz fields. The internal field is the sum of field…

Bekenstein bound from the Pauli principle

Assuming that the degrees of freedom of a black hole are finite in number and of fermionic nature, we naturally obtain, within a second-quantized toy model of the evaporation, that the Bekenstein bound is a consequence of the Pauli exclusion principle for these fundamental degrees of freedom. We show that entanglement, Bekenstein and thermodynamic entropies of the black hole all stem from the same approach, based on the entropy operator whose structure is the one typical of Takahashi and Umezawa's Thermofield Dynamics. We then evaluate the von Neumann black hole--environment entropy and notice…

An effective solution to convex $1$-body $N$-representability

From a geometric point of view, Pauli's exclusion principle defines a hypersimplex. This convex polytope describes the compatibility of $1$-fermion and $N$-fermion density matrices, therefore it coincides with the convex hull of the pure $N$-representable $1$-fermion density matrices. Consequently, the description of ground state physics through $1$-fermion density matrices may not necessitate the intricate pure state generalized Pauli constraints. In this article, we study the generalization of the $1$-body $N$-representability problem to ensemble states with fixed spectrum $\mathbf{w}$, in o…

Quon Statistics for Composite Systems and a Limit on the Violation of the Pauli Principle for Nucleons and Quarks

The quon algebra gives a description of particles, ``quons,'' that are neither fermions nor bosons. The parameter $q$ attached to a quon labels a smooth interpolation between bosons, for which $q = +1$, and fermions, for which $q = -1$. Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. Here we generalize this result to composite systems of identical quons. We find $q_{composite}=q_{constituent}^{n^2}$ for a system of $n$ identical quons. This result reduces to the …

高斯基函数用于原子的聚合物自洽场理论

Gaussian Basis Functions for a Polymer Self-Consistent Field Theory of Atoms

本文提出了一种基于高斯基函数的聚合物自洽场理论，用于计算原子的结合能和电子密度，并探讨了泡利不相容原理及量子动能校正的实现。

Pinning of Fermionic Occupation Numbers

The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970's, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundar…

探测扩展泡利原理的实验方案

Experimental proposal to probe the extended Pauli principle

本研究提出多量子点系统实验方案，以探测费米子波函数反对称性带来的泡利原理额外约束，同时为检验费米子量子信息处理及相关量子计算机架构能力提供试验场。

Quasi-pinning and entanglement in the lithium isoelectronic series

The Pauli exclusion principle gives an upper bound of 1 on the natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of kinematic nature, satisfied by these numbers. Here for the first time a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasi-pinned. For rank-six and rank-seven approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a ran…

Atomic shell structure from an orbital-free-related density-functional-theory Pauli potential

Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modelled as Gaussian threads with ring-polymer architecture in a four dimensional thermal-space, and a Pauli potential is postulated based on classical excluded volume implemented in the thermal-space using Edwards/Flory-Huggins interactions in a mean-field approximation. Other approximations include a Fermi-Amaldi correction for electron-electron self-interactions, a spherical averaging approximation to reduce the dimensionality of the…

Rotational invariance and the spin-statistics theorem

In this article the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics follows as a consequence of this coupling while the Bose-Einstein follows by breaking it. In section 5, the above approach is related…