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Atomic Nuclei: Nuclear Spin State Population Distribution

Atomic Nuclei: Nuclear Spin State Population Distribution

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.

Atomic Nuclei: Nuclear Spin State Overview

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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...

Atomic Nuclei: Types of Nuclear Relaxation

Atomic Nuclei: Types of Nuclear Relaxation

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...

Atomic Nuclei: Nuclear Relaxation Processes

Atomic Nuclei: Nuclear Relaxation Processes

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.

¹H NMR: Interpreting Distorted and Overlapping Signals

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...

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

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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...

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Related Experiment Video

Updated: Jul 26, 2025

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Fractionalized Prethermalization in a Driven Quantum Spin Liquid.

Hui-Ke Jin¹, Johannes Knolle^1,2,3, Michael Knap^1,2

¹Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany.

Physical Review Letters

|June 16, 2023

Summary

This summary is machine-generated.

Quantum spin liquids exhibit unique heating when driven, showing a two-step process called fractionalized prethermalization. This behavior arises from fractionalization and can be observed in quantum platforms.

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Area of Science:

Condensed Matter Physics
Quantum Information Science

Background:

Quantum spin liquids possess exotic fractionalized quasiparticles.
Periodic driving of quantum systems can lead to complex nonequilibrium dynamics.

Purpose of the Study:

Investigate the nonequilibrium heating behavior of a driven Kitaev honeycomb model.
Examine the dynamics of emergent Majorana matter and Z2 flux excitations.

Main Methods:

Analysis of a driven Kitaev honeycomb model.
Study of emergent Majorana and Z2 flux excitation dynamics.

Main Results:

Discovery of a two-step heating profile termed fractionalized prethermalization.
Observation of a quasistationary state with distinct matter and flux sector temperatures.
Attribution of prethermalization behavior to fractionalization.

Conclusions:

Fractionalization is key to the observed prethermalization in driven quantum spin liquids.
An experimental protocol is proposed for observing fractionalized prethermalization in quantum platforms.