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¹H NMR: Long-Range Coupling

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: 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: 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...

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,...

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...

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...

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Bulk-edge coupling in the non-Abelian nu=5/2 quantum hall interferometer.

B Rosenow¹, B I Halperin, S H Simon

¹Physics Department, Harvard University, Cambridge 02138, Massachusetts, USA.

Physical Review Letters

|July 23, 2008

Summary

Probing non-Abelian statistics in quantum Hall effect requires understanding quasiparticle behavior. Strong coupling restores interference patterns in Fabry-Perot interferometers by enabling Majorana fermion tunneling.

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Area of Science:

Condensed Matter Physics
Quantum Information Science

Background:

Non-Abelian statistics are crucial for topological quantum computation.
Quantum Hall effect edge states host quasiparticles with exotic statistics.
Fabry-Perot interferometers are used to probe these quasiparticles.

Purpose of the Study:

Analyze the impact of Majorana fermion tunneling on quantum Hall interferometer interference patterns.
Investigate the role of coupling strength between bulk and edge states.
Explore tunability of this coupling via experimental parameters.

Main Methods:

Theoretical analysis of quasiparticle tunneling in a quantum Hall Fabry-Perot interferometer.
Modeling the effect of neutral Majorana fermion coupling between bulk and edge states.
Investigating the dependence of interference patterns on coupling strength and source-drain voltage.

Main Results:

Weak coupling of Majorana fermions degrades the interference signal.
Strong coupling leads to the absorption of bulk quasiparticles by edge states.
The interference signal is fully restored at strong coupling.
Coupling strength is tunable by the applied source-drain voltage.

Conclusions:

Strong coupling regimes offer a viable pathway for robustly probing non-Abelian statistics.
The Fabry-Perot interferometer, under specific coupling conditions, can overcome signal degradation.
Tunable coupling via voltage presents a method for controlling and optimizing these quantum measurements.