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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,...
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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...
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Trapped two-dimensional condensates with synthetic spin-orbit coupling.

Subhasis Sinha1, Rejish Nath, Luis Santos

  • 1Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia 741252, India.

Physical Review Letters
|January 17, 2012
PubMed
Summary
This summary is machine-generated.

We investigate trapped 2D atomic Bose-Einstein condensates, revealing novel phases like half-vortex solutions and stripe phases. These emerge from the interplay of spin-orbit coupling, confinement, and interactions.

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Area of Science:

  • Quantum physics
  • Atomic physics
  • Condensed matter physics

Background:

  • Bose-Einstein condensates (BECs) are quantum states of matter formed by cooling atoms to near absolute zero.
  • Spin-orbit coupling introduces a dependence of particle momentum on its spin orientation.
  • Trapped 2D BECs provide a controllable platform for studying quantum phenomena.

Purpose of the Study:

  • To explore the rich physics of trapped 2D atomic Bose-Einstein condensates with spin-independent interactions.
  • To investigate the effects of isotropic spin-orbit coupling on BEC properties.
  • To understand the interplay between spin-orbit coupling, confinement, and interatomic interactions.

Main Methods:

  • Theoretical study of trapped 2D atomic Bose-Einstein condensates.
  • Analysis of systems with spin-independent interactions and isotropic spin-orbit coupling.
  • Examination of different interaction regimes (low, intermediate, strong repulsive).

Main Results:

  • Two types of half-vortex solutions with distinct winding numbers observed in low interaction regimes.
  • A stripe-phase, analogous to homogeneous condensates, emerges with strong repulsive interactions.
  • An hexagonally-symmetric phase with a triangular lattice of density minima appears in intermediate regimes with significant spin-orbit coupling.

Conclusions:

  • The interplay of spin-orbit coupling, confinement, and interactions leads to diverse quantum phases in 2D atomic BECs.
  • The observed phases, including half-vortices and stripe/hexagonal phases, are tunable via interaction strength and spin-orbit coupling.
  • These findings offer insights into quantum many-body physics and potential applications in quantum simulation.