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

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 Constant: Overview

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 Coupling

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,...

Atomic Nuclei: Nuclear Spin State Overview

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: Three-Bond Coupling (Vicinal Coupling)

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...

NMR Spectroscopy: Spin–Spin Coupling

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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Updated: Jun 5, 2026

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

Spin-orbit coupled spinor Bose-Einstein condensates.

Chunji Wang¹, Chao Gao, Chao-Ming Jian

¹Institute for Advanced Study, Tsinghua University, Beijing, 100084, China.

Physical Review Letters

|January 15, 2011

Summary

This summary is machine-generated.

Researchers explored spin-orbit coupling in cold atom systems, observing unique structures in Bose-Einstein condensates. They identified two distinct phases, one with vortices and broken time-reversal symmetry, and another with spin stripes.

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Area of Science:

Atomic physics
Quantum mechanics
Condensed matter physics

Background:

Spin-orbit coupling is crucial for understanding quantum phenomena.
Cold atom systems provide a controllable platform for studying fundamental physics.
Bose-Einstein condensates (BECs) exhibit unique quantum properties.

Purpose of the Study:

To investigate the effects of Rashba spin-orbit coupling on spin-1/2 and spin-1 Bose-Einstein condensates.
To identify and characterize different phases and structures within these condensates.
To understand the role of inter-boson interactions in phase transitions.

Main Methods:

Engineering atom-light interactions to generate spin-orbit coupling.
Numerical simulations to analyze condensate wave functions and identify phases.
Analytical methods to understand the observed phenomena and determine transition points.

Main Results:

Nontrivial structures develop in the condensate wave function under Rashba spin-orbit coupling.
Two distinct phases were identified: one with a plane wave ground state, domain structures, vortices, and broken time-reversal symmetry; the other with a standing wave and spin stripes.
Interactions between bosons drive the transition between these two phases.

Conclusions:

Rashba spin-orbit coupling in cold atom BECs leads to complex emergent structures.
The identified phases and transitions offer insights into quantum many-body physics.
Analytical and numerical approaches successfully characterized the system's behavior and phase diagram.