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Related Concept Videos

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
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...
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.
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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Published on: February 10, 2017

Nonlocal Cooper pair splitting in a pSn junction.

M Veldhorst1, A Brinkman

  • 1Faculty of Science and Technology and MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

This study proposes perfect Cooper pair splitting using crossed Andreev reflection (CAR) in semiconductor-superconductor junctions. This method offers a high-quality source of entangled electron pairs for future quantum technologies.

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Area of Science:

  • Condensed matter physics
  • Quantum information science

Background:

  • Cooper pair splitting is crucial for generating entangled electron pairs.
  • Existing methods often suffer from low efficiency and purity.

Purpose of the Study:

  • To propose a novel method for perfect Cooper pair splitting.
  • To investigate the feasibility of using semiconductor-superconductor junctions for entanglement generation.

Main Methods:

  • Modeling the p-type semiconductor-superconductor-n-type semiconductor (pSn) junction using Bogoliubov-de Gennes equations.
  • Extending the Blonder-Tinkham-Klapwijk theory beyond the Andreev approximation.
  • Analyzing the crossed Andreev reflection (CAR) process.

Main Results:

  • Predicted perfect Cooper pair splitting due to energy filtering by electrode band structures.
  • Achieved significant CAR current despite large momentum mismatch.
  • Demonstrated 100% purity of the nonlocal current.

Conclusions:

  • The proposed pSn junction design enables high-quality Cooper pair splitting.
  • This approach provides a promising route towards high-quality sources of entanglement.
  • Potential applications in quantum computing and communication.