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.
"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…
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…
The validity of the Pauli Exclusion Principle, a building block of Quantum Mechanics, is tested for electrons. The VIP (VIolation of Pauli exclusion principle) and its follow-up VIP-2 experiments at the Laboratori Nazionali del Gran Sasso search for x-rays from copper atomic transition that are prohibited by the Pauli Exclusion Principle. The candidate events, if they exist, originate from the transition of a $2p$ orbit electron to the ground state which is already occupied by two electrons. The present limit on the probability for Pauli Exclusion Principle violation for electrons set by the V…
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…
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 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 underg…
The VIP (Violation of Pauli exclusion principle) experiment and its follow-up experiment VIP-2 at the Laboratori Nazionali del Gran Sasso (LNGS) search for X-rays from Cu atomic states that are prohibited by the Pauli Exclusion Principle (PEP). The candidate events, if they exist, will originate from the transition of a $2p$ orbit electron to the ground state which is already occupied by two electrons. The present limit on the probability for PEP violation for electron is 4.7 $\times10^{-29}$ set by the VIP experiment. With upgraded detectors for high precision X-ray spectroscopy, the VIP-2 ex…
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…
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 …
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…
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 …
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…
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…
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…
Equal-spin and opposite-spin density-density correlations in the BCS-BEC crossover: Gauge Symmetry, Pauli Exclusion Principle, Wick's Theorem and Experiments
Rhineland-Palatinate Technical University Kaiserslautern-Landau（莱茵兰-普法尔茨凯泽斯劳滕-兰道理工大学）；Georgia Institute of Technology（佐治亚理工学院）
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…
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…
In this paper, we analyze the evolution of the generalized Pauli channels governed by the memory kernel master equation. We provide necessary and sufficient conditions for the memory kernel to give rise to the legitimate (completely positive and trace-preserving) quantum evolution. In particular, we analyze a class of kernels generating the quantum semi-Markov evolution, which is a natural generalization of the Markovian semigroup. Interestingly, the convex combination of Markovian semigroups goes beyond the semi-Markov case. Our analysis is illustrated with several examples.
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…
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 …
Color code thresholds under circuit-level noise beyond the Pauli framework
INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Institute for Complex Quantum Systems, Ulm University（乌尔姆大学复杂量子系统研究所）；Padua Quantum Technologies Research Center, Università degli Studi di Padova（帕多瓦大学帕多瓦量子技术中心）
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…
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…
QMCtwin: Master-Equation Simulation of Syndrome Statistics Beyond Pauli Noise
University of Southern California（南加州大学）；Center for Quantum Information Science & Technology, University of Southern California（南加州大学量子科学与技术中心）；Quantum Elements, Inc.（量子元素公司）；Harvard University（哈佛大学）；AWS Worldwide Specialist Organization（亚马逊云科技全球专家组织）
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…
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…
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…
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…
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…
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…
We show that the covariance matrix of a quantum state can be reconstructed from position measurements using the simple notion of polar duality, familiar from convex geometry. In particular, all multidimensional Gaussian states (pure or mixed) can in principle be reconstructed if the quantum system is well localized in configuration space. The main observation which makes this possible is that the John ellipsoid of the Cartesian product of the position localization by its polar dual contains a quantum blob, and can therefore be identified with the covariance ellipsoid of a quantum state.
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…
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…
