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Related Concept Videos

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...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
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...
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,...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...

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Molecular Entanglement and Electrospinnability of Biopolymers
07:59

Molecular Entanglement and Electrospinnability of Biopolymers

Published on: September 3, 2014

Optimal spin squeezing inequalities detect bound entanglement in spin models.

Géza Tóth1, Christian Knapp, Otfried Gühne

  • 1ICFO-Institut de Ciències Fotòniques, E-08860 Castelldefels (Barcelona), Spain.

Physical Review Letters
|February 1, 2008
PubMed
Summary

Researchers identified all generalized spin squeezing inequalities, crucial for detecting entanglement in unaddressable spin-1/2 particle systems and revealing bound entanglement in thermal spin states.

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Area of Science:

  • Quantum information science
  • Condensed matter physics

Background:

  • Entanglement is a key quantum resource, but its detection can be challenging in systems with unaddressable particles.
  • Generalized spin squeezing inequalities offer a potential avenue for entanglement detection.

Purpose of the Study:

  • To derive the complete set of generalized spin squeezing inequalities.
  • To establish these inequalities as entanglement criteria for spin-1/2 systems.
  • To explore their application in detecting bound entanglement in thermal spin states.

Main Methods:

  • Theoretical derivation of generalized spin squeezing inequalities.
  • Analysis of their properties as entanglement witnesses.
  • Application to thermal states of spin models.

Main Results:

  • The complete set of generalized spin squeezing inequalities has been determined.
  • These inequalities serve as effective entanglement criteria.
  • The study demonstrates their utility in identifying bound entanglement in thermal spin states.

Conclusions:

  • The derived inequalities provide a comprehensive tool for entanglement detection in challenging quantum systems.
  • This work advances the understanding and experimental verification of entanglement, particularly bound entanglement.