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Atomic Nuclei: Nuclear Spin State Overview01:03

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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...
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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.
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All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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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...
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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.
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Coherent spin qubit shuttling through germanium quantum dots.

Floor van Riggelen-Doelman1, Chien-An Wang1, Sander L de Snoo1

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Area of Science:

  • Quantum Information Science
  • Solid-State Physics
  • Quantum Computing Hardware

Background:

  • Networked quantum computing relies on quantum links to interconnect qubit registers.
  • Semiconductor quantum dot qubits show promise but face challenges in establishing robust quantum links.
  • Hole spin qubits in germanium are a potential platform, but strong spin-orbit interaction poses difficulties.

Purpose of the Study:

  • To demonstrate the feasibility of qubit shuttling for establishing quantum links in semiconductor quantum dots.
  • To investigate the preservation of quantum information during qubit shuttling in a germanium-based system.
  • To overcome the challenges posed by spin-orbit interaction in germanium hole spin qubits.

Main Methods:

  • Utilizing a minimal quantum dot chain to shuttle hole spin qubits.
  • Shuttling both spin basis states and superposition states of the qubits.
  • Employing dynamical decoupling techniques to extend the coherence length of shuttled qubits.

Main Results:

  • Successfully shuttled spin basis states over effective lengths exceeding 300 microns.
  • Demonstrated coherent shuttling of superposition states over effective lengths of 9 microns.
  • Extended the coherent shuttling distance to 49 microns using dynamical decoupling.

Conclusions:

  • Qubit shuttling is an effective strategy for routing qubits within registers.
  • The demonstrated technique facilitates the establishment of quantum links between registers.
  • Germanium hole spin qubits are a viable platform for quantum networking applications.