"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-fermion states are randomly prepared on the quantum computer and tested for constraint violations. Measurements show no violation and confirm the generalized Pauli exclusion principle with an error of one part in one quintillion.
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…
VIP2 in LNGS - Testing the Pauli Exclusion Principle for electrons with high sensitivity
Gran Sasso地下实验室（LNGS）的VIP 2（泡利不相容原理的VIolation）实验正在以非常高的灵敏度寻找原子中可能违反标准量子力学预测的情况。为了验证泡利不相容原理（PEP）和相关的自旋统计定理，我们用精密的X射线光谱研究了原子跃迁。我们将介绍我们的实验方法来寻找铜原子中的"异常"（即保利禁戒）X射线跃迁，由"新"电子产生，它可能有很小的概率经历保利禁戒跃迁到已经被两个电子占据的基态。我们将描述VIP 2实验装置，该装置目前正在LNGS获取数据。VIP2的目标是以前所未有的准确度测试PEP中的电子，直到PEP被违反的概率限制在10 $^{-31}$的水平。我们将介绍目前的实验结果，并讨论可能违反的影响。
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
泡利不相容原理-2实验的VIOLATION，或VIP-2实验，在Gran Sasso的Nazionali del Gran Sasso实验室寻找来自铜原子跃迁的X射线，这是泡利不相容原理所禁止的。候选的直接破坏事件来自于一个$2p$电子到已经被两个电子占据的基态的跃迁。从VIP-2实验2016年的第一次数据采集活动中，我们确定了3.4 $\times$ × 10 $^{-29}$的最佳上限，用于存在这种违规的概率。实验系统学的控制也取得了显着的改善，虽然没有明确反映在改进的上限。通过在分析中引入信号和背景数据的同时光谱拟合，我们成功地考虑了以前在这种类型的测量中无法评估的系统误差。
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…
Recently predicted and observed Pauli crystals are structures formed by trapped ultracold non-interacting particles obeying Fermi statistics. The relative positions of the particles are determined by the trapping potential and the Pauli exclusion principle. Measuring all particles at once, their positions tend to be close to vertices of non-trivial polyhedrons. Similar shapes are found for systems of particles bound to the surface of a sphere.
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…
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…
It has been conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures, called Pauli crystals, are predicted for a two-dimensional system of free fermions under harmonic confinement. It is assumed that the system consists of neutral fermionic atoms with their spins frozen (spin-polarized) in order to avoid any form of electromagnetic interaction. These crystalline patterns emerge as the most frequent configurations seen in a la…
