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The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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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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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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Spin–Spin Coupling Constant: Overview01:08

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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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Quantum Numbers02:43

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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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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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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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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.
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Toward Programmable Quantum Processors Based on Spin Qubits with Mechanically Mediated Interactions and Transport.

F Fung1, E Rosenfeld1, J D Schaefer1

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Researchers developed a new method for controlling quantum information using nitrogen-vacancy (NV) centers in diamond coupled to mechanical resonators. This approach enables entanglement and programmable connections for scalable quantum computing.

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Area of Science:

  • Quantum Information Science
  • Materials Science
  • Nanotechnology

Background:

  • Solid-state spin qubits, like nitrogen-vacancy (NV) centers in diamond, are promising for quantum computing.
  • Achieving controlled interactions and entanglement in large multiqubit systems remains a significant challenge.

Purpose of the Study:

  • To present a novel method for programmable control and entanglement of multiqubit spin systems.
  • To explore the coupling of NV-center qubits with nanomechanical resonators for quantum information processing.

Main Methods:

  • Coupling individual NV centers in diamond nanopillars to magnetically functionalized silicon nitride mechanical resonators.
  • Utilizing mechanical transport of qubits for programmable connectivity.
  • Characterizing mechanical properties and magnetic field gradients of the nanomechanical system.
  • Demonstrating coherent spin qubit manipulation and detecting time-varying magnetic fields using NV centers.

Main Results:

  • Achieved a spin-mechanical coupling of 7.7(9) Hz between an NV center and an oscillating micromagnet.
  • Demonstrated coherent manipulation of a spin qubit in proximity to a transported micromagnet.
  • Verified the feasibility of using nanomechanical resonators for qubit entanglement and programmable connectivity.

Conclusions:

  • The proposed method offers a new pathway for scalable quantum information processing with solid-state spin qubits.
  • Realistic improvements can lead to reaching the high-cooperativity regime, crucial for advanced quantum applications.
  • This work paves the way for enhanced control and entanglement in multiqubit systems.