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Related Concept Videos

Composite Bodies00:55

Composite Bodies

A composite body is a body made up of multiple parts, connected to form a larger, unified object. Each part has its own weight and center of gravity, which must be considered to determine the center of gravity of the composite body. In cases where the density or specific weight is constant, the center of gravity coincides with the centroid.
Composite bodies have widespread applications in mechanical engineering, from automobiles to aircraft to rockets. For example, an automobile wheel comprises...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...

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Related Experiment Video

Updated: Jun 14, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Entanglement and composite bosons.

Christopher Chudzicki1, Olufolajimi Oke, William K Wootters

  • 1Department of Physics, Williams College, Williamstown, Massachusetts 01267, USA.

Physical Review Letters
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Entanglement in fermion pairs dictates their bosonic behavior. Stronger entanglement, indicated by density matrix purity, drives fermion pairs closer to behaving like elementary bosons.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Setting Limits on Supersymmetry Using Simplified Models

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Last Updated: Jun 14, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Published on: November 15, 2013

Area of Science:

  • Quantum mechanics
  • Atomic physics
  • Condensed matter physics

Background:

  • Fermions are fundamental particles that obey the Pauli exclusion principle.
  • The behavior of multiple fermions can sometimes mimic that of bosons under specific conditions.
  • Previous work by C. K. Law explored aspects of fermionic systems.

Purpose of the Study:

  • To generalize the understanding of how entanglement affects the bosonic character of fermion pairs.
  • To establish bounds on a quantity that quantifies this bosonic behavior.
  • To link entanglement measures to the degree of bosonic behavior in fermionic systems.

Main Methods:

  • Derivation of upper and lower bounds for the ratio chi{N+1}/chi{N}.
  • Analysis of the single-particle density matrix purity as a measure of entanglement.
  • Theoretical investigation of N pairs of fermions sharing a wave function.

Main Results:

  • Established bounds on the quantity chi{N+1}/chi{N}, which governs bosonic character.
  • Demonstrated that these bounds are dependent on the purity of the single-particle density matrix.
  • Showed that high entanglement leads to chi{N+1}/chi{N} approaching the ideal bosonic value.

Conclusions:

  • Entanglement is a key factor determining if a fermion pair can exhibit bosonic properties.
  • The purity of the single-particle density matrix serves as a quantifiable indicator of entanglement's role.
  • Sufficiently entangled fermion pairs can effectively behave as elementary bosons.