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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: 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,...

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...

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...

Atomic Nuclei: Nuclear Spin State Population Distribution

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.

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Updated: Jun 3, 2026

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

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

Published on: August 2, 2019

Robust quantum state transfer in random unpolarized spin chains.

N Y Yao¹, L Jiang, A V Gorshkov

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

Physical Review Letters

|March 17, 2011

Summary

We introduce a novel quantum state transfer method using random spin chains to couple remote spin qubits. This approach enables robust, long-range, and perfect state transfer without individual spin control.

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Last Updated: Jun 3, 2026

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

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

Published on: August 2, 2019

Area of Science:

Quantum Information Science
Solid-State Physics
Quantum Computing

Background:

Efficient quantum state transfer is crucial for scalable quantum information processing.
Current methods often require complex control or are limited in range and robustness.
Developing new protocols for reliable qubit coupling is a key challenge in quantum computing.

Purpose of the Study:

To propose and analyze a novel approach for quantum state transfer between remote spin qubits.
To demonstrate the feasibility of achieving coherent quantum coupling using random spin chains.
To investigate the robustness and applicability of this method in solid-state systems.

Main Methods:

Theoretical analysis of quantum coupling via random, unpolarized spin chains.
Hamiltonian evolution for achieving state transfer over arbitrary distances.
Numerical simulations and analysis of realistic imperfections and decoherence effects.

Main Results:

Demonstrated that random spin chains can facilitate coherent quantum coupling between remote qubits.
Showcased robustness against coupling-strength disorder and the need for individual spin control.
Achieved strong coherent coupling between nitrogen-vacancy centers at room temperature over micrometer distances.

Conclusions:

The proposed method offers a promising route for long-range, perfect quantum state transfer.
Applicability in solid-state quantum information processors, particularly with nitrogen-vacancy centers.
The approach is robust to disorder and does not require complex individual spin manipulation.