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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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 Relaxation Processes01:23

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

Atomic Nuclei: Nuclear Spin State Overview

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 one, the...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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 have a...
Atomic Nuclei: Nuclear Magnetic Moment00:59

Atomic Nuclei: Nuclear Magnetic Moment

All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Spontaneous circulation in ground-state spinor dipolar Bose-Einstein condensates.

Yuki Kawaguchi1, Hiroki Saito, Masahito Ueda

  • 1Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan.

Physical Review Letters
|October 10, 2006
PubMed
Summary

Researchers studied spin-1 ferromagnetic Bose-Einstein condensates with magnetic dipole interactions. They discovered three ground-state phases, including spontaneous chiral symmetry breaking and orbital angular momentum. These findings are observable in 87Rb condensates.

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Area of Science:

  • Atomic physics
  • Quantum mechanics
  • Condensed matter physics

Background:

  • Bose-Einstein condensates (BECs) are quantum states of matter formed by cooling bosons to near absolute zero.
  • Spin-1 BECs exhibit complex magnetic properties due to their internal spin structure.
  • Magnetic dipole-dipole interactions introduce long-range, anisotropic forces in BECs, influencing their phase behavior.

Purpose of the Study:

  • To investigate the ground-state phases of a spin-1 ferromagnetic Bose-Einstein condensate (BEC) incorporating magnetic dipole-dipole interactions.
  • To explore the emergence of orbital angular momentum and chiral symmetry breaking in such systems.
  • To identify experimental conditions for observing these predicted phases in a realistic BEC system.

Main Methods:

  • Solving the nonlocal Gross-Pitaevskii equations numerically.
  • Analyzing the system's ground-state properties across different parameter regimes.
  • Investigating the role of magnetic dipole-dipole interactions and trap parameters.

Main Results:

  • Identification of three distinct ground-state phases in the spin-1 ferromagnetic BEC.
  • Observation of spontaneous chiral symmetry breaking.
  • Emergence of substantial orbital angular momentum in a specific parameter range.
  • Prediction of experimental observability in spin-1 87Rb condensates.

Conclusions:

  • The interplay of spin-1 ferromagnetism and magnetic dipole-dipole interactions leads to rich phase diagrams in BECs.
  • Chiral symmetry breaking and orbital angular momentum are key emergent phenomena in these systems.
  • Experimental tuning of atom number or trap frequency can realize these predicted phases in 87Rb BECs.