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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.
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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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 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...
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NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

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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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π Electron Effects on Chemical Shift: Overview01:27

π Electron Effects on Chemical Shift: Overview

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An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
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Atomic Nuclei: Nuclear Spin State Overview01:03

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...
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Updated: Oct 11, 2025

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Beyond-Mean-Field Effects in Rabi-Coupled Two-Component Bose-Einstein Condensate.

L Lavoine1, A Hammond1, A Recati2

  • 1Laboratoire Charles Fabry, UMR 8501, Institut d'Optique, CNRS, Université Paris-Saclay, Avenue Augustin Fresnel, 91127 Palaiseau CEDEX, France.

Physical Review Letters
|December 3, 2021
PubMed
Summary
This summary is machine-generated.

We explore beyond-mean-field effects in Bose-Einstein condensates (BECs). Rabi coupling modifies the energy density, revealing new two- and three-body interactions crucial for stabilizing BEC mixtures.

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Area of Science:

  • Quantum physics
  • Atomic physics
  • Condensed matter physics

Background:

  • Bose-Einstein condensates (BECs) are quantum states of matter.
  • Beyond-mean-field (BMF) effects are crucial for understanding BECs.
  • Two-component BECs with tunable interactions are ideal for studying BMF physics.

Purpose of the Study:

  • To theoretically calculate and experimentally measure the BMF equation of state in a coherently coupled two-component BEC.
  • To investigate the role of Rabi coupling in modifying the BMF energy density.
  • To observe the emergence of new two- and three-body interactions.

Main Methods:

  • Theoretical calculations of the BMF equation of state.
  • Experimental measurements using a coherently coupled two-component BEC of 39K.
  • Analyzing the expansion dynamics of the BEC with and without Rabi coupling.
  • Investigating the density and Rabi-coupling frequency (Ω) dependence of the energy density.

Main Results:

  • The BMF energy density transitions from Lee-Huang-Yang scaling to integer power-law scaling with increasing Ω.
  • A novel two-body BMF term (∝n^2√Ω) and a repulsive three-body term (∝n^3/√Ω) were identified.
  • Experimental evidence for these contributions was obtained from the expansion dynamics of a Rabi-coupled 39K condensate.
  • Rabi coupling was shown to preserve spin composition, preventing drift from the vanishing mean-field point.

Conclusions:

  • Rabi coupling plays a critical role in controlling BMF effects in two-component BECs.
  • The observed two- and three-body interactions provide new insights into quantum many-body physics.
  • Rabi coupling offers a method to stabilize BEC mixtures, enabling the study of phenomena in systems with spin-asymmetric losses.