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Related Concept Videos

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.
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.
¹³C NMR: ¹H–¹³C Decoupling01:04

¹³C NMR: ¹H–¹³C Decoupling

The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
A broadband decoupling technique is used to simplify these complex, sometimes overlapping, signals. Broadband decoupling relies on a...
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...
Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...

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Real-time Observation of the DNA Strand Exchange Reaction Mediated by Rad51
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Subradiant split Cooper pairs.

Audrey Cottet1, Takis Kontos, Alfredo Levy Yeyati

  • 1Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS UMR 8551, Laboratoire associé aux universités Pierre et Marie Curie et Denis Diderot, 24, rue Lhomond, 75231 Paris Cedex 05, France.

Physical Review Letters
|June 12, 2012
PubMed
Summary

We propose a method to measure the coherence of split Cooper pairs from a double-quantum-dot Cooper pair splitter (CPS). Observing the CPS

Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Nanotechnology

Background:

  • Cooper pair splitters (CPS) are crucial for quantum information processing.
  • Characterizing the coherence of split Cooper pairs is essential for advancing quantum technologies.
  • Existing methods for coherence characterization may be limited in scope or applicability.

Purpose of the Study:

  • To develop and demonstrate a novel method for characterizing the coherence of Cooper pairs emitted by a double-quantum-dot based CPS.
  • To investigate the radiative response of a CPS coupled to a microwave cavity as a probe for Cooper pair coherence.
  • To explore the potential generalization of this technique to other nanoscale electronic circuits.

Main Methods:

  • Utilizing a double-quantum-dot Cooper pair splitter (CPS) integrated within a microwave cavity.

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  • Analyzing the radiative response of the CPS as a function of its coupling to the cavity.
  • Employing principles of cavity quantum electrodynamics to interpret the coherence signatures.

    • Main Results:

    • Demonstrated that the coherence of split Cooper pairs strongly influences the emitted radiation.
    • Observed a characteristic nonmonotonic variation in radiation output directly linked to Cooper pair coherence.
    • Established a direct correlation between cavity coupling parameters and the coherence properties of the split pairs.

    Conclusions:

    • The radiative response of a CPS in a microwave cavity provides a sensitive measure of Cooper pair coherence.
    • Cavity quantum electrodynamics offers a powerful framework for probing coherence in nanoscale quantum circuits.
    • This technique holds promise for characterizing coherence in a broader range of quantum devices and systems.