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Atomic Nuclei: Nuclear Relaxation Processes01:23

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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.
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Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, or glass.
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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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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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Collective excitations in two-component ultracold quantum matter.

Avinaba Mukherjee1, Subhendu Saha1, Raka Dasgupta1

  • 1Department of Physics, University of Calcutta, 92 A. P. C. Road, Kolkata 700009, India.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|May 22, 2025
PubMed
Summary

Collective oscillations in ultracold quantum gases reveal critical behaviors. Studying these collective modes, like density and spin modes, offers insights into exotic phases and pairing structures in two-component systems.

Keywords:
BCS-BEC crossoverBose–Einstein condensatecollective dynamicsoscillation modes

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Area of Science:

  • Quantum Physics
  • Condensed Matter Physics
  • Ultracold Atomic Gases

Background:

  • Two-component ultracold quantum gases exhibit complex collective behaviors.
  • Understanding these behaviors is key to exploring exotic quantum phases.

Purpose of the Study:

  • Review theoretical works on collective oscillations in two-component ultracold quantum gases.
  • Investigate the emergence of critical phenomena and exotic phases.
  • Highlight the utility of collective oscillations as experimental probes.

Main Methods:

  • Theoretical review of collective oscillations.
  • Analysis of density and spin modes in bosonic and fermionic systems.
  • Focus on Goldstone and roton modes, including roton softening.
  • Examination of striped phases and population-imbalanced fermionic phases (FFLO, breached pair).

Main Results:

  • Two primary collective modes identified: density and spin modes.
  • Demonstration of mode conversion to Goldstone modes, indicating criticality.
  • Discussion of roton mode emergence and softening in various mixtures.
  • Characterization of exotic fermionic phases and their collective excitations.

Conclusions:

  • Collective oscillations in two-component quantum gases provide critical insights.
  • These oscillations serve as valuable indirect probes for exotic phases and structures.
  • Further study can elucidate pairing structures and imbalance in fermionic systems.