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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: 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: 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...
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.
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...
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved in...

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Superfluid pairing gap in strong coupling.

J Carlson1, Sanjay Reddy

  • 1Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

Physical Review Letters
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

Researchers measured the zero-temperature pairing gap in imbalanced Fermi systems. The gap was found to be larger than in any other Fermi system studied, exceeding 0.4 times the Fermi energy.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Simulation
  • Ultracold Atomic Gases

Background:

  • The zero-temperature pairing gap is a key property of interacting fermions, essential for testing many-body theories in the strong coupling regime.
  • Understanding this gap is crucial for characterizing superfluidity in fermionic systems.

Purpose of the Study:

  • To experimentally determine the zero-temperature pairing gap in imbalanced Fermi systems at unitarity.
  • To compare this gap with values found in other fermionic systems.

Main Methods:

  • Analysis of recent cold-atom experiments on imbalanced Fermi systems.
  • Utilizing Quantum Monte Carlo results for superfluid and normal phases.
  • Extraction of the pairing gap in the fully paired superfluid state at infinite scattering length (unitarity).

Main Results:

  • The experimental zero-temperature pairing gap was determined for the first time at unitarity.
  • The pairing gap was found to be greater than 0.4 times the Fermi energy (E(F)).
  • A preferred value of (0.45 ± 0.05) E(F) was identified, representing the largest ratio of pairing gap to Fermi energy observed to date in any Fermi system.

Conclusions:

  • The study provides a critical experimental benchmark for theoretical models of strongly interacting Fermi systems.
  • The results highlight the unique properties of fermionic systems at unitarity.
  • This work advances the understanding of superfluidity in quantum simulations.