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arXiv:quant-ph/0006130 · Physical Review A

Inequalities for electron-field correlation functions

Tomáš Tyc

Published Jun 8, 2000• 0 citations
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Abstract

We show that there exists a class of inequalities between correlation functions of different orders of a chaotic electron field. These inequalities lead to the antibunching effect and are a consequence of the fact that electrons are fermions: indistinguishable particles with antisymmetric states. The derivation of the inequalities is based on the known form of the correlation functions for the chaotic state and on the properties of matrices and determinants.

DOI
10.1103/physreva.62.013803

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We show that there exists a class of inequalities between correlation functions of different orders of a chaotic electron field. These inequalities lead to the antibunching effect and are a consequence of the fact that electrons are fermions: indistinguishable particles with antisymmetric states. The derivation of the inequalities is based on the known form of the correlation functions for the chaotic state and on the properties of matrices and determinants.
We consider the situation in which the field of quantum particles such as photons (bosons) or electrons (fermions) undergoes a significant attenuation during the detection process. We characterize the second-order statistical properties of the field by the bunching for bosons and the antibunching for fermions. Bunching and antibunching effects are derived from the time intervals distributions of the random point process of detection instead of the moments of the number of particles registered in a given time interval. Fields of both beams are supposed to be in chaotic states and have second-order time correlation functions of exponential profile and of arbitrary correlation time. A test is proposed for nonclassical states: the behavior of the antibunching function is a nondecreasing function near the origin of the time axis.
We theoretically study the high-order correlation functions of chaotic bosons and fermions. Based on the different parity of the Stirling number, the products of the first-order correlation functions are well classified and employed to represent the high-order correlation function. The correlation of bosons conduces a bunching effect, which will be enhanced as order NNN increases. Different from bosons, the anticommutation relation of fermions leads to the parity of the Stirling number, which thereby results in a mixture of bunching and antibunching behaviors in high-order correlation. By further investigating third-order ghost diffraction and ghost imaging, the differences between the high-order correlations of bosons and fermions are discussed in detail. A larger NNN will dramatically improve the ghost image quality for bosons, but a good strategy should be carefully chosen for the fermionic ghost imaging process due to its complex correlation components.
Bosons have symmetric wave function under particle exchange, while fermions have antisymmetric wave functions. This leads to differences in behavior of the two kinds of particles even in the gaseous state. Strong repulsive forces between atoms at close range are due to the Pauli principle that forbids two electrons to be in the same energy or position state. A repulsive Pauli pressure operates similarly in white dwarf stars. Bosons undergo Bose–Einstein condensation because of Bose statistics. The wave function symmetry of particles with spin can affect the magnetic states and the behavior of transport properties, for example, viscosity and thermal conductivity. The symmetry properties of bosons at a beam splitter are demonstrated in the Hong–Ou–Mandel effect or in a Michelson interferometer via the Hanbury Brown-Twiss effect. Researchers see boson bunching and fermion antibunching in experiments considered.
We explore the relationship between symmetrization and entanglement through measurements on few-particle systems in a multiwell potential. In particular, considering two or three trapped atoms, we measure and distinguish correlations arising from two different physical origins: antisymmetrization of the fermionic wave function and interaction between particles. We quantify this through the entanglement negativity of states, and the introduction of an antisymmetric negativity, which allows us to understand the role that symmetrization plays in the measured entanglement properties. We apply this concept both to pure theoretical states and to experimentally reconstructed density matrices of two or three mobile particles in an array of optical tweezers.