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Related Concept Videos

Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
694
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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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.
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...
971
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

1.0K
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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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

1.1K
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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Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

1.0K
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,...
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Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

340
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
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Optimal Spin Polarization Control for the Spin-Exchange Relaxation-Free System Using Adaptive Dynamic Programming.

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    This study introduces a new adaptive dynamic programming method to control 3-D spin polarization in atomic ensembles. This approach enables achieving arbitrary spin states by leveraging multiphysics fields.

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    Area of Science:

    • Quantum physics
    • Atomic physics
    • Control theory

    Background:

    • Controlling 3-D spin polarization in atomic ensembles is crucial for advanced applications.
    • Existing methods face challenges with complex field interactions and asymmetric input constraints.

    Purpose of the Study:

    • To develop a novel method for 3-D spin polarization control (3DSPC) in atomic ensembles.
    • To achieve arbitrary spin polarization states by utilizing multiphysics fields.

    Main Methods:

    • Proposed a novel adaptive dynamic programming (ADP) structure using a multicritic multiaction neural network (MCMANN) with nonquadratic performance functions.
    • Formulated the 3DSPC problem as a multiplayer nonzero-sum game (MP-NZSG) under asymmetric saturation input constraints.
    • Developed and proved the convergence of the multicritic multiaction ADP (MCMA-ADP) algorithm using the compression mapping principle.

    Main Results:

    • Successfully implemented the MCMA-ADP algorithm for 3DSPC.
    • Demonstrated the algorithm's ability to achieve arbitrary spin polarization states.
    • Validated the theoretical findings through numerical simulations in a spin-exchange relaxation-free (SERF) system.

    Conclusions:

    • The proposed MCMA-ADP algorithm effectively solves the 3DSPC problem.
    • This method offers precise control over spin polarization states by exploiting multiphysics fields.
    • The findings pave the way for enhanced control in quantum technologies and atomic systems.