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Related Concept Videos

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:
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...
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,...
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...

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Related Experiment Video

Updated: Jul 13, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Perfect quantum state transfer with spinor bosons on weighted graphs.

David L Feder1

  • 1Department of Physics and Astronomy and Institute for Quantum Information Science, University of Calgary, Calgary, Alberta T2N 1N4, Canada.

Physical Review Letters
|December 13, 2006
PubMed
Summary

Quantum particles can efficiently navigate complex networks, traversing infinite hierarchies of graphs with perfect probability. This discovery enables efficient quantum state transfer, even with exponentially increasing network sizes.

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Related Experiment Videos

Last Updated: Jul 13, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Area of Science:

  • Quantum physics
  • Network theory
  • Condensed matter physics

Background:

  • Exploring quantum particle behavior on lattices and graphs is crucial for quantum information science.
  • Understanding quantum state transfer is key to developing quantum communication and computation.

Purpose of the Study:

  • To reveal a duality between spinor bosons on lattices and single particles on weighted graphs.
  • To demonstrate efficient quantum state transfer across complex network structures.

Main Methods:

  • Investigating a duality between many-body systems and single-particle systems on graphs.
  • Analyzing quantum particle traversal on an infinite hierarchy of networks.
  • Discussing experimental implementation using ultracold atoms in optical lattices.

Main Results:

  • A quantum particle can traverse infinite networks with perfect probability in polynomial time.
  • Network traversal efficiency is maintained despite exponentially increasing node numbers.
  • Special cases include one-dimensional quantum wires and hypercubes.

Conclusions:

  • The established duality provides a powerful framework for understanding quantum transport in complex networks.
  • Efficient quantum state transfer is achievable, paving the way for advanced quantum technologies.